The book is quite old (written in 1950, revised 1977) but for the most part has aged well. (My main complaints are using "he" and "man" as a neutral and some outdated racial terminology). This is a relatively academic book that surveys existing work from several centuries, and advances some theories of its own.
I think the most interesting theory is that anxiety generally relates to inner conflicts or repressed hostility. I've realized that a lot of my anxiety stems from the conflict between wanting people to like me and wanting people to do things for me (e.g. asking people for things causes me anxiety because I want them to help me, but I worry that asking firmly will cause them to dislike me). I also have the reverse issue, that when people ask me to perform a task I don't want to, I have a conflict between wanting to please them but not wanting to perform the task. This largely comes up in a work context and admittedly does lead to some repressed hostility.
He also mentions how our specific culture values individualist competitive success, and how this leads to much anxiety (despite this pressure to succeed, individuals ultimately don't have control over the economic conditions around them). There's even a mention of sado-masochism as a reaction to the anxiety from our competitive capitalist society.
He also touches on the idea that some level of anxiety is normal and fine, and that the difference between normal and pathologic anxiety is that normal anxiety is proportional to the threat. In either case, he proposes that anxiety should not be avoided or repressed, but should be moved through to achieve greater self-development.