Upvote:3
It depends on the languages you can read. The best book that I know is in Russian:
Alexei Tolochko, Essays on the original Rus,
Толочко А. П. Очерки начальной руси. Киев; Санкт-Петербург, Лаурус, 2015.
And in Ukrainian:
Наталья Николаевна Яковенко, Нарис Історії України. З найдавніших часів до кінця XVIII століття (Essay of the history of Ukraine from the ancient times to XVIII century).
One problem with the history of Kievan Rus, is that this subject is highly politically charged. This "history" was originally created with a political purpose: to confirm the rights of the ruling dynasty. Then in 17-18 centuries, the Moscow state "appropriated" this history, and even the name Rus, and since then, the "history" was used mostly to prove the right of Moscow to rule the territory which used to be Kievan Rus.
This did not change to this day. For this reason I do NOT recommend reading only Russian (Moscow) authors. In the writings of Ukrainian authors the point of view is very different, though some Ukrainian authors may be biased in another direction. (The author that I recommend is least biased on my opinion: he lives and works in Ukraine, but writes in Russian. Not to be confused with his father, P. Tolochko).
Speaking of Western authors, I can recommend
whose initial chapters are on Kievan Rus.
When searching for Western authors, I recommend to search on "History of Ukraine", rather than "History of Russia", unless you want to read the Moscow propaganda retold by a Western author.
Another problem is almost complete lack of original sources. The main source is the so-called "Original chronic", which was written centuries after the events it describes, and also under the sponsorship of the ruling dynasty. Foreign sources are extremely scarce.
Having all this in mind, you can certainly read this original chronic, or any modern exposition of it.
Remark: the more correct tag for this question is "history of Ukraine" not "history of Russia". (Kiev is in Ukraine, as we all know). So I added the tag.