For a different perspective, I would recommend The Crusades through Arab eyes by Amin Maalouf.

My go to intro texts are:

Thomas Asbridge The Crusades, this one is my preferred history. It goes into good depth on all of the big Crusades as well as quite a few of the later, less well remembered ones.

Jonatahn Riley-Smith The Crusades: A Short History, I recommend this one if you don't have a lot of free time and want a more succinct history that hits on all the big events but doesn't go into quite as much detail and trails off pretty abruptly after the Third Crusade.

Steven Runciman A History of The Crusades, 3 volumes, Despite it's great length this is not the superior academic work of these three. Originally written in the '50s Runciman's history is a bit out of date these days. However, Runciman was an excellent writer and they're a wonderful read. I recommend this series usually to people who find reading dense histories boring and are okay trading a bit of accuracy for some quality writing.

If you want more in depth histories of specific topics I'd recommend the following:

Malcolm Barber The New Knighthood, Barber is sort of the historian of the Knight's Templar and this is his big work on the order. I must admit I haven't read it, yet, but it comes highly recommended and is high on my queue of books to read. He's also written a history of the Crusader States that looks very good.

Conor Kostick The Siege of Jerusalem, This one I haven't read as well but Dr. Kostick was one of my undergrad lecturers and the stuff of his I've read in the past was all very good. This is a short history but it includes a lot of detail and some good images of 11th century siege equipment.

Anne Marie-Edde Saladin, the definitive biography of Saladin is an excellent book not just on the Sultan but on the age and area in which he lived. The one qualifier I'd put on this work is that you need a basic understanding of the first three Crusades before you read this book as Edde does not hold your hand and explain everything. She assumes you are familiar with the fall of Jerusalem and the Race for Egypt, for example.

for the slightly more obscure crusader historian i'd recommend:

the northern crusades by eric christiansen is a good book about the armed struggle between the german and nordic christians against the pagan wends and the orthodox slavs & the teutonic order by william urban is an extensive overview of the germanic military order.