Russian Republic

The Russian Republic is one of two main forces that are currently engaged in the prolonged Russian Civil War with Soviet Russia over who exactly will be the sole remaining (and thus, the legitimate) successor to the now dead Russian Empire. It is however, in fact, merely a provisional state, perpetually frozen in this mid-way form due to the ongoing war.
The Russian Constituent Assembly, while succesfully elected and allowed to began its work, ultimately has devolved into a political stalemate. While it managed to elect the change of the provisional Russian Republic into the Russian Democratic Federative Republic, the decree never went fully into effect as nothing besides that was achieved due to resistance from both Bolsheviks in the Assembly and militant extreme right groups outside.
Because of that, the Russian Republic officially still exists, even though it has lost significant parts of its territory following the May Revolution.

Structure

The Russian Republic was supposed to be a provisional form of a state during the transition period between the abdication of Tsar Nicholas II and the creation of a new form of state, achieved through popular vote and the creation of the Russian Constituent Assembly. It was supposed to govern the Russia in the interim, while making sure that the country remains in the Great War and keeps a significant part of the Central Powers army occupied on the Eastern Front.
Because of that it was governed by the so called Provisional Government, that was supposed to keep the country running until the elections to the Constituent Assembly. The first government was formed by Georgy Lvov and consisted mostly of Kadets (Constitutional Democrats). After the first cabinet collapsed, the socialists seized power under Aleksandr Kerensky.
This government, in turn, fell during the May Revolution when Kerensky and most of his cabinet was assasinated and the already ailing Constituent Assembly was scattered around. It was replaced - in at best apartially democratic manner - by Lavr Kornilov, who remains minister-president to this day.
The Provisional Government remains an absolute power over the Russian Republic that is, however, exactly as strong as its army. It is a de facto military dictatorship under Lavr Kornilov, created and upheld with the intention of unifying Russia again and calling for a Constituent Assembly once again, in hope of creating a democratic representation of all Russia's population.
PG is composed of sixteen ministries. Trade and Industry, Foreign Affairs, Internal Affairs, War, Navy, Finance, Justice, Transport, Education, Agriculture, Labour, Food, Health Care, Posts and Telegraphs, Religion, and Winter. The most important ministries are those of War, Internal Affairs, and Winter, due to on-going war that they are instrumental in.
The legislative power is the Council of the Russian Republic, at least on paper. It was officially dismantled following the creation of the Constituent Assembly and wasn't brought back (officially) after its collapse. The current Council is not an official organization, with Lavr Kornilov grabbing all power he needed to have the Republic continue its fight against the Reds. It's still quite respected and serves as the representation of political parties... but mostly of the socialist ones.

Public Agenda

The only agenda of Kornilov's government is surviving against Soviet Russia and winning the Russian Civil War. In any way possible. However, the part about remaining a democratic state after that becomes less and less possible, as not only is the Republic a military dictatorship currently, it's also torn apart by internal strife between socialists, liberal democrats and recently resurgent monarchist-reformists.

History

The Russian Republic was proclaimed after the abdication of Tsar Nicholas II. At first, the Provisional Government role was to serve as the transitional government between one monarch and another. However, the Republic began turning towards the political left more and more. Firstly, the monarchy was abolished. Then constitutional democrats were forced out of it and were replaced by all manners of socialists, both democratic and revolutionary.
Then it was almost ousted by the sudden Bolshevik (even more militant socialists) uprising that interrupted the Constituent Assembly action to establish a new (socialist) government and a new Russia. Freezing the Republic in its mid-way state and forcing it to suffer under a de facto military dictatorship. While this is by no means a tyrannical dictatorship, that does not change everything.
In recent times, despite at least some successes on the front, the Russian Republic is in an increasingly problematic position. While Lavr Kornilov's authority remains unquestioned - as all political groups agree that the Bolsheviks are a common threat that must be eliminated no matter what - there is an increasing political strife centered around the question of "what then?".
On one side there are socialists. Socialist-Revolutionary Party (or at least its center-right faction, as the so called Left SR together with big part of the center joined Bolsheviks) and other socialists/communists They won a decisive victory in the Constituent Asembly, with SR getting 40.4% of votes (7.7 more was taken by the Ukrainian SR), mensheviks getting 2.6% (plus 1.5% taken by Georgijan mensheviks) and 0.9% by other, minor groups.
They are still the strongest political movement, mostly responsible for the current Provisional Government... but they are losing ground due to steady progress of the monarchist-reformists that are slowly eradicating the SR from the villages. While strongest, they are slowly losing and fading away.
Then, there are kadets. The Constitutional Democrats, a party of various liberal democrats that want to establish Russia as a democracy... but are against 'socialist ideas' for the government and want to make Russia more like West. While they got less than 5% of the votes in the elections for the Constituent Assembly, that was because of the number of Russians living in the rural areas. They were - and remained to this day - a party strong in cities, outclassing SR massively and with only Bolsheviks (supported by various workers and lower strata) being able to face them. They managed to gain some supporters from the socialists in the cities, but remain behind other two movements.
The third and unexpected addition are the so called monarchists-reformists. While initially pushed into nothingness (especially right after abdication of the vastly unpopular Nicholas II), they resurged after the May Revolution. Part of their supporters are faithful Orthodox that see the Bolsheviks (that are slowly getting more and more insane) as God's punishment for overthrowing the Tsar. Others are various remaining aristocrats and nobles, whose power was crippled from the land reforms of the post-Bolshevik Provisional Government. Others are people that want strong government, some of whom actually believe that Russian Republic proves that Russian people aren't ready for democracy.
They push for a constitutional (but strong) monarchy under either the overthrown Tsar Nicholas, his son Alexei or the Tsar's youngest brother, Michael. They are increasingly popular amongst the military, especially the 'russian warlords', with merely Wrangel being closer to kadets (and he isn't even in Russia) and Antonov being a staunch socialist. This causes increasing fear amongst the socialists, especially as the grey eminence of the Ministry of Winter, the Father Frost, Grigorij Rasputin seems to favour them as well...

Demography and Population

The biggest problem of the Russian Republic is that most of its territory is Siberia. Not only it lacks significant industrial areas (with exception of mines), but also population. Because of that, Russian Republic army is permanently outnumbered, and the biggest problem of the government is to make sure there are enough recruits (and equipment to arm them).
While majority of citizens are Russians, it is a very small majority. Various siberian and central asian people (tribes, even) form significant part of population and are used as recruitment ground especially for cavalry. Their ambitions (that seem to be forming, albeit slowly) are another problem the Republic is going to face.

Military

The 'official' Russian Army collapsed entirely following the bolshevik revolution. While Lavr Kornilov managed to take over what remained, a significant part of his forces are actually loyal to various warlords that emerged in the transition period. While the most successful one (Untern von Sternberg) is no longer part of the Republic, there are still many strong people, elevated high by their own strength and achievements and sometimes having small 'personal' armies. They are sometimes called vohzds.
They listen to the orders from the Ministry of War... if only to get access to new recruits and weapons. Examples of such important warlords include Georgij Semyonov in the Transbaikal, Denikin in the west and Alexandr Kolchak in the Far East. Yudenich and Wrangel can be counted into it as well, but officially their forces are a part of the Central Powers.

Religion

Orthodox Church is dominant, though a lot of sects play some role. There are also a lot of pagans, especially in deeper parts of Siberia. Church role in the Russian Republic is minimal, it would gladly condemn it due to its mostly socialist government if not for the fact, that bolsheviks are even worse than it. It, however, plays important role in the monarchist-reformist movement, and at least Mikhail Diterikhs sees the war against the communist as holy war against the heathens (gaining a lot of Church attention).

Foreign Relations

Russian Republic stopped being part of Entente following the Weimar Congress when it signed peace treaty with Central Powers, officially (though bitterly) resigning from Baltic States, Poland, Right-bank Ukraine and Belarus. It was hard decision, despite the Republic not controlling the territory in question - but it was sweetened by the fact that in exchange Central Powers committed themselves to not recognize the Soviet Russia as a political entity. And were ready for at least limited cooperation.
Russian Republic stopped being a part of the Great War... theoretically. It signed Treaty of Anchorage to gain access to industrial might of United States of America. For now it is focused on trying to win the Russian Civil War.
Its current approach to Central Powers is relatively bitter... but Entente is downright hated, especially amongst those politically active nad the vohzds. The locals didn't forget the Entente's 'help' - like the lack of recognition of Kornilov's government until United States gave it, cutting short their supply of weapons after Reds were proven to continue the Eastern Front, and the almost idiotic attempts of brokering a peace treaty between Reds and Whites... not to mention the brief period during which Entente was closer to establishing political relationships with Reds, seeing them as a 'true representation of Russian nation".

Agriculture & Industry

Ailing and heavily relying on support from Entente. Especially United States. Siberia has a lot of natural resources it can export, but it lacks heavy industrial centers of the Central Russia and agricultural might of Ukraine.

Trade & Transport

Pretty much entirety of it depends on the Trans-Siberian Railway and the port in Vladivostok. Losing it means losing everything.

Important Characters

Provisional Government
Lavr Kornilov
Minister-President. De facto dictator of Russia and a man that tries to keep it together to defeat the Reds... and then reinstate the Republic. Probably.

Grigorij Rasputin
Major Awakened and a Minister of Winter. Great enigma that one day returned from the dead... bringing Winter-based thaumaturgies to save the Russia from the Reds.

Vohzds
Georgij Semyonov
Ataman of Baikal Cossacks. Widely seen as a close compatriot of the insane Roman Untern von Sternberg. With his cavalry being seen by many as little more than thugs... but dangerous thugs.

Anton Denikin
Commander of Volunteer Army. While pushed from Southern Russia east, he remains a cornerstone of the Russian Republic frontline with the Reds. Decidedly ambitious, but with Reds close to him, he is more or less pacified.

Alexandr Kolchak
Leader of the Russian Far East. De facto commander of everything left from Russian Navy, tasked with making sure that nothing interrupts the lifeline of the Trans-Siberian Railway and the port in Vladivostok - while simultaneously making sure that Empire of Japan won't try to make border corrections... again.

Nikolai Yudenich
Commander of the Northwestern Army. Extreme reactionary, that almost captured the Petrograd during the first days of the May Revolution. Now, a commander of White forces fighting besides German Empire.

Pyotr Vrangel
Former cavalry commander, promoted to a leader of Russian White Army in Poland and Ukraine after Reds defeated Whites in the Southern Russia (where he fought with great skill, delaying them for a while and forcing them to besiege him on Crimean Peninsula).

Mikhail Diterikhs
Leader of the Holy Army in Siberia, a growing host of soldiers that see the war against the Reds as a religious 'crusade', taking in more and more of Orthodox zealots from all parts of Russia.

Alexander Antonov
A rare case of former bolshevik supporter that quit them after seeing their deeds up close. Leader of the Tambov peasant rebellion that was required almost a hundred thousand Reds to be finally squashed... and even then, he retreated with most of his forces intact behind the Whites lines, and struck and unlike (and probably temporary) alliance with Kornilov...

Boris Savinkov
Head of People's Army of Russia. His forces combine Russian nationalism with elements of socialism (though, admittedly, being ready to proceed with agrarian reform is enough to be considered socialist amongst the Whites). His national socialism longs for strong government, but a democratic one. While an outsider, he is most ready to put aside his beliefs to oppose Reds...

Jewgienij Miller
Commander of the so called Northern Army. Evacuated from Murmansk and Arkhangielsk after it was obvious that it could not hope to defend itself, mostly with United States help. A rare combination of all political groups, he remains loyal to Kornilov.

Others
Nicholas II
Former tsar. Deposed and de facto imprisoned, he was taken out of the prison after the Rasputin ressurection as a pivotal point of thaumaturgical radio propaganda targeted at peasants... which caused his slowly growing support amongst the masses.