Name a good European history book

A friend of mine complains that their history education was spotty. So, I thought I’d get them a book about European history for Xmas.

I was thinking of something along the lines of an AP European History textbook, like you’d get as a student, but I am not sure what to go for. And, a straight-up school textbook might not be the most fun gift. I might still go that way, but would like to consider some options.

Got any suggestions? I’m generally looking for something that covers the period from the Dark Ages to the 20th century.

Tony Judt Postwar

Its not textbook but its great history

After Tamerlane by John Darwin. It’s a bit advanced but a great read if you know the general developments since 1400.
Agree on Judt’s Postwar–but the war it refers to is the Second World War.
I’d suggest any Western Civilization course textbook used at the undergrad level. They give you the nitty-gritty and usually have nice charts, maps, and illustrations. I’d recommend for one Lynn Hunt et al’s The Making of the West.
For 20th century, Judt, and Mark Mazower is very good, but somewhat advanced. I see lots of praise for Paxton’s 20th century textbook, as well as for the old standbys–Hobsbawm, Lichtheim…

Millennium: From Religion to Revolution: How Civilization Has Changed Over a Thousand Years by Ian Mortimer is an interesting book. Mortimer doesn’t attempt to tell a complete history of western civilization over a thousand year period - a task which is pretty much impossible for a single volume. Instead, he discusses what he sees as the most important changes that arose in each century. I highly recommend it.

eta: Millenium is the title of the paperback edition. The original hardcover edition was titled Centuries of Change: Which Century Saw the Most Change and Why It Matters to Us.