Grigori Rasputin was a Russian monk and mystic who managed to win the confidences of the Russian royal family and played a significant role in the family's demise.
The last Russian Czar, Nicholas II, and his wife Alexandra had several daughters but only one son, Alexis, who was the heir apparent. Sadly, Alexis suffered from hemophilia, and was constantly ill. His mother obsessed over his health, so much so that she seldom let him walk outside, rather she had him carried by a Russian sailor. Rasputin was introduced to the family by Alexandra's sister, who insisted that he was a miracle worker. Rasputin could stop Alexis' bleeding, apparently by hypnotizing him which caused him to relax.
Rasputin was often sexually promiscuous, often coercing members of the Royal court to have sex with him, which caused a great deal of discord. He also interfered a great deal in government decisions while Nicholas was away by his influence over Alexandra, who tended to believe his every word. On one occasion, Alexandra wrote to Nicholas
believe in our friend. He lives for you and Russia.
Alexandria herself was opposed to parliamentary government and attempted to rule while Nicholas was at the front during World War I. Rasputin's constant presence and obvious interference caused the Russian people to increasingly lose faith in their government and move closer to Revolution.
Rasputin was assassinated by a member of the royal family in hopes of restoring some degree of confidence in the government. Sadly, events had gone too far. Rasputin did not cause the revolution, but his meddling in government affairs exacerbated an already difficult situation.
An excellent resource on Rasputin is The Life and Times of Grigori Rasputinby Alex DeJonge.
As the author of a book on Rasputin, after 12 years of research, I can tell you that Rasputin had nothing to do with the revolution and had nothing to do with the Tsar's demise. He had been murdered before either of those things happened. He was not a monk, but a 'strannik', a wandering spiritual pilgrim, of which there were many at that time.
Don't forget there had been a revolution in 1905, before Rasputin ever came to the capital. Both that one and the one in 1917 were about the Tsar's disregard for his people, other than the aristocracy. Most Russians had to work long hours, under horrific conditions, with little food. The Jews, with few exceptions, were confined to a ghetto called the Pale of Settlement and were denied educations, most occupations and, of course, their choice of where to live. In addition, the Tsar sanctioned 'pogroms' - regular raids on Jewish villages wherein entire families were tortured and slaughtered, for no other reason than antisemitism.
Nicholas II was an indecisive and weak leader and made many poor decisions, but he never took Rasputin's advice, except on spiritual matters and his son's health. Like the Tsar, most of the aristocracy was very antisemitic. They had an ingrained hatred of Jews. Rasputin advocated equal rights for the Jews, much to the horror of the nobility, and he was vilified for it. The nobles spread rumors about him being promiscuous and a drunkard, despite the fact that many of them had numerous affairs and drank vodka and champagne copiously. The rumors hit the newspapers in the form of political cartoons which drew Rasputin as demonic, greedy, ugly and evil - the very same way they depicted Jews in the media.
Rasputin did make suggestions about appointing cabinet members. He recommended people who were against war, as he was, and who would legislate equal rights for the Jews. The Tsar chose to engage in war and refused to give Jews equal rights.
The revolution happened because the people were tired of an oppressive existence, while the nobility lived in opulence. Rasputin had nothing to do with it. After the revolution, the Jews were given equal rights and no longer had to live in the Pale, although other issues would arise in time. All those associated with the revolution stated that it was ridiculous to think that a revolution would be caused by one man. Such thinking was just a denial of the country's numerous problems.
Most books on the subject, including the Alex DeJonge book, like to exploit the myth, as it makes for sensationalist reading and great book sales. Many authors and screen writers have embroidered on the myth for effect. You can read the books by Maria Rasputin, but of course, she loved her father. R.J. Minney wrote a fairly decent biography. Dr. Elizabeth Judas, who knew Rasputin, wrote a bio called "Rasputin - Neither Devil Nor Saint". She derides him for his aid to the Jews, but confirms his efforts. Or, you could read my book, "Rasputin and The Jews: A Reversal of History".