Unless you can read Russian (and have an access to Russian bookstore), now there are so few experts in pre-modern Russia in anglophone countries.

• Martin, Janet. Medieval Russia. 2nd ed. Cambridge: Cambridge UP, 2007 (1st ed. 1993): While it is a bit dry, it is in fact only the affordable and the most accessible choice for later Middle Ages under 'the yoke of the Tatars' to early Muscovite period in Russian History (the author originally specializes in socio-economic history).
• Crummey, Robert O. Formation of Muscovy 1300-1613. London: Longman (now Routledge), 1987. Longman History of Russia 3: A bit dated (published before the collapse of USSR).
• Ostrowski, Donald & Marshall Poe (eds.). Portraits of Old Russia: Imagined Lives of Ordinary People, 1300-1745. London: Routledge, 2011: Though it is technically not a academic research work, it may be very interesting to read for the better understanding in pre-modern Russian society. It is actually a collective (pseudo-) biographies written by the specialists of pre-modern Russia, based on their research on the primary sources and the academic literature. Ostrowski is now almost the only very active Anglo-Phone researcher in Russian history, from the 15th to the 17th century, so his other books are also worth checking.

Notes upon Russia (link to the 19th century English translation), written by the ambassador of the Habsburgs, Sigismund von Herberstein who visited Moscovy in person, is also a very valuable account of Russia during the period you asked in OP, though we should also take his bias into consideration.