Russian is written using the Cyrillic Alphabet, named after a 6th Century Missionary Monk from Greece, St. Cyril, who adapted his native Greek alphabet to produce something that could be used by illiterate Slavs, Bulgars and others that he took his message to in the Balkans - so that the Bible could be written down for them. The alphabet was exported northwards to Russia, along with the Orthodox religion. When the Mongolian Khan Nogai attacked Constantinople in 1264AD, large numbers of Byzantine Monks and Scholars fled to Russia, the second Orthodox nation after Greece, and there was a new wave of Greek influence on the language, alphabet and culture. The modern Russian alphabet came into use in the 1920's when many obsolete old letters were dropped and a major reform of spelling took place, making Russian spelling completely logical, with just one exception - "-oro" on the ends of words, which looks like it ought to be pronounced "ogo", but in fact comes out as "ovo".
Below is the Cyrillic alphabet in typed and cursive form. Pay particular attention to some of the differences that happen from the typed to cursive letters. They might just cause you some problems if you aren't aware of them. For example the cursive letter "t" is written "m". Also, cursive letter "L" comes out as an upside-down "V", "/\", and a lower case letter "p" comes out in cursive Russian as "n". Confusing maybe at first but in just a short time you know the letters like a native. Good luck and enjoy learning a little something about your ladies wonderful language.