Alexander I was the son of
Emperor Paul of
Russia, but his early life was more controlled by his grandmother
Catherine the Great. She named him (after
Alexander Nevsky) and took him to raise her way, much as Empress
Elizabeth had taken Paul to raise herself. Catherine's way included studying
Enlightenment philosophers as Catherine herself had (though Catherine did not really implement those beliefs in her rule). Alexander's tutors said he had difficulty concentrating, and his formal schooling ended at 16 when Catherine arranged a
marriage for him.
Paul and Catherine did not get along, and Alexander learned diplomacy trying to deal with both of them. Catherine discussed skipping Paul in the succession and naming Alexander her heir, but Alexander told his father that he didn't want to do this. However, when Catherine died in 1796 and Paul became Emperor, Alexander's radical politics began to disagree more and more with his father's. A group of conspirators (who probably told Alexander they were going to depose and imprison the Emperor) murdered Paul in his palace in 1801 and so Alexander became Emperor.
However, having his father murdered made Alexander a little paranoid. His politics became more middle of the road; although he often mentioned the possibility of creating a constitution for Russia, he never went through with it and always retained absolute power. Alexander was polite to everyone and wanted to be popular with nobles, commoners, and foreign countries, which sometimes made him seem inconsistent when he told everyone what they wanted to hear. He put a lot of foreigners into government positions (to the point that when he asked a Russian general what would be the best reward for the general's services, the respsonse was, "Sire, make me a German.")
Alexander did put many popular reforms into place -- he allowed non-nobles to buy land, stopped peasants on government land from being given to private landowners, and reformed education. However, he was dedicated enough to monarchy to be the only European ruler to send a protest to France when a member of the French royal family was executed for conspiring against Napoleon in 1804. Russian troops later marched against Napoleon in Europe, but were defeated and an unpopular (in Russia) peace treaty was signed in 1807. The enmity did not end, and Napoleon invaded Russia in 1812, but his troops were not able to withstand the Russian winter without supplies, and Russia was just too big to take city-by-city. By 1815, the conflict with France was over, and Alexander became a major power in Europe. This was the reactionary period of his reign, as he forced military men and their families to live in rural villages, prohibited Freemasons and other secret societies, and censored books and university professors.
Alexander had no surviving children, nor did his next-younger-brother Constantine, so he privately named his brother Nicholas as heir in 1819 because Nicholas had a son. In 1825, Alexander took a trip to the south of Russia to visit the Crimea. He caught a chill there and died on 19 November 1825 (though there is a legend that he did not die, but rejected the throne and became a monk; this probably arose because Alexander was usually in excellent health) and Nicholas I became Emperor. Because Alexander had not publicized his naming of Nicholas as heir, there was confusion in Russia and some swore oaths to Constantine as Emperor before the news got out that it was Nicholas.
Sources: Donald Raleigh and A.A. Iskenderov's The Emperors and Empresses of Russia: Rediscovering the Romanovs and those listed under Monarchs of Russia.