The first thing that came to my mind: Russia still holds a naval base located in Syria, which is of a special strategic value, as is Russia's the only one in the Mediterranean region. Well, how did Russians acquire it?
The desire for warm water ports, suggested by the commenters, dates back to Ivan the Terrible and Livonian War.
It was satisfied after almost 150 years, when Piotr I defeated Sweden in Great Northern War. The successful wars with Ottoman Empire, which secured a safe access to Black Sea, started in the second half of 17th century and lasted through the 18th. Through all these years there were 3 main directions of Russian expansion:
- Central Europe - holding Polish-Lithuania as a de facto protectorate, then its dissolution, then holding status quo through the 19th century, secured by cgood relations with Prussia and Austria
- Far East - securing Siberia and Pacific Coast, trying to be an active player of Chinese politics
- South - expansion towards Caucasus, Balkans, straits of Bosfor/Dardanele and Central Asia (dreaming of liberating Constantinople and reaching shores of Indian Ocean)
Let's consider the last one - the territory of Syria, until the early 20th century part of Ottoman Empire, did never play any important part in Russian politics, whether the rulers were tzars or pre-ww2 Soviets. The territories of importance back then were Balkans, the Straits, Central Asia, Iran, Afghanistan, Georgia/Armenia/Azerbaijan - logically, laying closer to Russia.
The situation was changed by Suez Crisis, as its result, Russians gained an alliance with president Naser, and the latter achieved and held what he wanted - Suez Channel nationalization. This events (failed intervention of Israelis and western forces) put Soviets at one of the sides of tense Middle East relations. That's IMHO the main reason for Soviet-Syriac alliance: then through the 50s, 60s, 70s USSR sent Syria large amounts of money, arms, and resources. It was a part of a larger plan - as the support (resources, arms, specialists) went also to other anti-Israeli (and anti-US) states as Egypt, Iraq, Libya.
Things changed in 70s and 80s, as Soviets were reproaching Syria's intervention in Lebanon. Besides weakened USSR of Chernienko and Gorbachev (80s) had troubles itself (Afghanistan, economy), and simply could not afford backing Syria's quarrelsome politics, its tense relations with Israel, and involvement in affairs of Lebanon.
The alliance went practically dead in 90s, the first visit of Assad in Moscow after the fall of Soviet Union took place in 99!
Putin tried to back Syria recently, as he's generally more politically active/aggresive than Yelzin (and Russia's economy is in much better condition now); tries to reconstruct the Soviet influence all over the places it was significant 20 years ago.
(I'll try to elaborate more on last 2 paragraphs later)
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