User Experience (UX) design underpins all good web design.  Good UX can be derived from experience, theory and research.  To get it right, it pays to validate it through User Testing and to iterate on those learnings.  There have been hundreds of books written on the subject but I've picked out four classics that everybody involved in web design should have read.  

The Design of Everyday Things by  Donald A. Norman

https://www.goodreads.com/book/show/840.The_Design_of_Everyday_Things

This seminal work doesn't focus on web design but is an excellent start on your journey to design things better.  

Even the smartest among us can feel inept as we try to figure out the shower control in a hotel or attempt to navigate an unfamiliar television set or stove. When The Design of Everyday Things was published in 1988, cognitive scientist Don Norman provocatively proposed that the fault lies not in ourselves, but in design that ignores the needs and psychology of people. 

Don't Make Me Think by Steve Krug 

http://www.sensible.com/dmmt.html 

This is not optional.  Every web designer should read this classic.  With DMMT we move from the theoretical to the specific.  How to make websites usable. 

Web designers have relied on usability guru Steve Krug’s guide to help them understand the principles of intuitive navigation and information design. Witty, commonsensical, and eminently practical, it’s one of the best loved and most recommended books on the subject. 

Rocket Surgery Made Easy: The Do-It-Yourself Guide to Finding and Fixing Usability Problems

http://www.sensible.com/rsme.html

Designing with usability in mind is one thing, but user testing is important to make sure the users are following your designs.  User testing is traditionally very expensive but in Krug's follow up book we see some techniques to carry out some guerrilla testing on a tighter budget. 

It's been known for years that usability testing can dramatically improve products. But with a typical price tag of $5,000 to $10,000 for a usability consultant to conduct each round of tests, it rarely happens. 

In this how-to companion to Don't Make Me Think: A Common Sense Approach to Web Usability, Steve Krug spells out an approach to usability testing that anyone can easily apply to their own web site, application, or other product. (As he said in Don't Make Me Think, "It's not rocket surgery".)

Designing for Emotion

https://abookapart.com/products/designing-for-emotion

This book first landed at KindlemanHQ for Christmas in 2011.  It focuses on creating an emotional connection with the user.  This book helps you take your design beyond usability and create engaging sites and apps that users love.  

Go beyond the basics—functionality, reliability, and usability—and design for humans, not machines. Learn how to express your brand’s personality and delight your audience through emotional design. 

Just Enough Research

https://abookapart.com/products/practical-design-discovery

No time was ever wasted on reconnaissance, as they say.  Well, maybe it's possible to overdo it, but not if you do Just Enough. Erika's book walks you through how to carry out effective research. 

Good research is about asking more and better questions, and thinking critically about the answers. It’s something every member of your team can and should do, and which everyone can learn, quickly. And done well, it will save you time and money by reducing unknowns and creating a solid foundation to build the right thing, in the most effective way.

Conclusion

So that's the list.  5 books that cover usability fundamentals, web design usability, usability testing, Research and designing for emotion to add engagement to the User Experience. There are many many more books out there though, If you think I missed a classic, let me know in the comments.