Greetings! This is certainly a critical question when it comes to understanding the polarisation of Europe in the decade or so leading up to 1914, and of all the bilateral relations on the continent, Russo-German ties (and hence tensions) can be slightly more complicated to unravel. For further reading, as parts of this response do link to other country's foreign policies during the timeframe discussed, consider this previous response on the breakdown of Austro-Hungarian-Russian relations, and this 'shortened summary' of the Russo-German fallout. Let's begin however, by picking up on the strands of the question which OP has laid down for us.

The Three Emperors

"[A]s long as the general European status quo did not alter too much, the Tsar [Alexander III] did not regard Russia's isolation seriously."

- Historian Laurence B. Packard writing on the Russo-German-Austrian relationship in the late 1800s.

This sentiment is one which is crucial to understand. The Russian Empire at the turn of the 20th century was facing an uncertain future in terms of its role on the continent. For St. Petersburg, their outward expansion into the Caucasus and Central Asia had led to clashes with Great Britain in the past few decades, most notably during the Crimean War of 1853 - 1856. This so-called "Great Game" (which I elaborate on here) meant that Russia was viewed with great suspicion by both Britain and France, as the two nations loathed the Tsar's ambitions to expand into the Black Sea region and threaten their presence in the Mediterranean.

This focus of foreign policy formed part of the "Eastern Question", the concern over the integrity of the flagging Ottoman Empire and how the Western European powers would deal with the threat rising from Eastern Europe. With the Russo-Turkish War of 1877-1878, this became a particular concern of foreign policymakers in London. In that war, Russian troops had come tantalisingly close to their "dream" of re-conquering Constantinople for the Orthodox Christian world and securing Russia's place as the "New Rome" so to speak. However, a Royal Navy squadron in the Bosphorus and repeated warnings from Britain caused the Tsar to back down, and led to the Congress of Berlin. At this conference, British Prime Minister Benjamin Disraeli humiliated the Russians by forcing them to accept Ottoman terms for peace and give up much of the territory they had conquered during the war (Disraeli even went so far as to threaten war with Russia if Alexander II did not acquiesce). Naval historian Andrew Lambert on this curious bit of policy from the British:

"Ever since the fall of the Byzantine Empire, Russian rulers had dreamt of restoring the city to Orthodox Christianity, of reconsecrating the Agia Sophia and of making themselves masters of the strategic hub of Eurasian land mass. But with [Admiral] Hornby's fleet on the Bosphorus, the Russians did not dare to seize the greatest prize that their army had ever laid eyes on. They had good reason not to move: while Hornby's four ships represented the Mediterranean fleet, the Channel fleet had been ordered to Malta and the third fleet was mobilising to attack St. Petersburg. Once the right arm of the British Empire flexed, Russia was paralysed. For all her military manpower and vast lands, Russia could not compete with British naval, economic, and industrial power."

So where did the Dreikaiserbund (League of the Three Emperors) factor into all of this? The League in essence provided some reassurance to St. Petersburg that whilst the Western European powers remained suspicious of Russian manoeuvres in the Balkans and the Straits, Central Europe - represented by the Austro-Hungarian Empire and the newly created German Empire - would not be too concerned with such ambitions.

The Dreikaiserbund came into being in 1881, and it was the brainchild of that master of realpolitik, Otto von Bismarck. Bismarck knew all too well that if he wished to maintain Germany's position in Central Europe and keep the balance of peace (which was always sketchy during that time period, especially with constant flare-ups over the Balkans), he needed to secure the goodwill of Tsar Alexander III. The Tsar for his part, trusted Bismarck, for the Iron Chancellor had no reason to go against Russian claims of influence in the Baltic. To him, the Balkans were a constant thorn in the side of European peace, and he personally did not wish to drag Germany into a scuffle with Russia over this matter. In fact, Alexander III and his advisers believed that Germany could actually be relied upon to oppose Austro-Hungarian expansionism in the Balkans, for the Habsburg monarchy was often the archrival "Great Power" to the Romanov dynasty when it came to Eastern Europe. Bismarck made constant reassurances to Alexander III that despite the existence of the Triple Alliance (between Germany, Austria-Hungary, and Italy), Russia would not be the target or an obstacle in any of their foreign policies.

Yet even with these reassurances in place, the Bismarckian alliance systems of the 1870s and 1880s was still limited in its effectiveness by that "powderkeg of Europe: the Balkans. Both Austria-Hungary and Russia had overlapping designs for the region, and Germany knew that if tensions between Vienna and St. Petersburg reach a point beyond mediation, then Berlin would have to come down on one side or the other. It is to this "cracking" of the Dreikaiserbund, and the fall of the Reassurance Treaty that we turn to next.

Part 1 of 3