Spartan Reflections by Paul Cartledge, who is the leading historian of ancient Sparta. It's an excellent collection of essays exploring different aspects of Spartan society.

https://www.youtube.com/watch?v=hVbDiQdLkxY

It's not a book, but a documentary done by the BBC. Part of the Ancient Worlds series done by Bettany Hughes. It's a two and a half hour overview of Spartan history. Bettany Hughes is certainly qualified, and total babe if that is your thing.

As someone else said Paul Cartledge is one of the best writers on sparta. I got it at barnes and noble when i was just looking for something to read on my train home and I am reading (like halfway through) it right now.

The Spartans: The World of the Warrior-Heroes of Ancient Greece

and its pretty solid.

looks around covertly

I don't know if i am allowed to recommend stuff like this here, so please note this is a more flippant response and the book is not a serious work of any historical accuracy or following any academic rigor, i just enjoyed it, but Steven Pressfield's Gates of Fire is a sick book about Thermopylae that keeps a "decent" historical edge. My more serious answer would be the Cartledge book but if you want some historical fiction on the side to make you want to learn even more Pressfield is your guy.