There are many Special relativity (SR) and General relativity (GR) textbooks, here I will review some of them.
SR introductory books
SR intermediate-advanced books
GR introductory books
GR intermediate books
GR advanced books
Historically influential books
Honourable mentions

Special relativity introductory books

1) Griffiths, David (2012). Introduction to Electrodynamics (4th ed.). Addison-Wesley. ISBN 978-0-321-85656-2.

Chapter 12- Electrodynamics and Relativity from this book is a very good introduction to SR. It is short and uses tensors to explain relativistic formulation of electrodynamics.

2) Resnick, ‎Robert (1968). Introduction to Special Relativity. Wiley.

This book discusses very slowly compared to the above one. If you have time you should read it. In the beginning, there is historical stuff that many books won’t discuss. Sadly it doesn’t use tensors to explain relativistic formulation of electrodynamics.

Special relativity intermediate-advanced books

1) Tsamparlis, Michael (2019). Special Relativity An Introduction with 200 Problems and Solutions (2nd ed.). Springer.

This book contains almost everything related to SR. It is more rigorous compared to the above books.

2) Günther, Helmut; Müller, Volker (2019). The Special Theory of Relativity: Einstein’s World in New Axiomatics. Springer.

It is at a similar level to the book by Tsamparlis.

General relativity introductory books

1) Carroll, Sean (2003). Spacetime and Geometry: An Introduction to General Relativity. ISBN 0-8053-8732-3. Reprinted 2019.

This book is a very good introduction to GR. It has the right mixture of pedagogy and formalism. The last chapter Quantum Field Theory (QFT) in Curved Spacetime discusses things which usual introductory books either leave or discuss just intuitively.

2) Hobson; Efstathiou; Lasenby (2006). General Relativity: An Introduction for Physicists. Cambridge University Press.

This book is at a similar level to Carroll’s, but it doesn’t discuss QFT in Curved Spacetime. Instead, the remaining parts are more complete than Carroll’s.

3) Ryder, Lewis (2009). Introduction to General Relativity. Cambridge University Press.

This book is at a similar level to Carroll’s. It is similar in style to Ryder’s QFT book.

4) D’Inverno, Ray (1992). Introducing Einstein’s Relativity. Oxford University Press.

This book is slightly easier and at a lower level than to the above books. Still a good book.

General relativity intermediate books

1) Padmanabhan, Thanu (2010). GRAVITATION FOUNDATIONS AND FRONTIERS. Cambridge University Press.

This book is somewhat more complete and rigorous than Carroll’s. It discusses QFT in Curved Spacetime. In the end, there is a chapter on emergent gravity(the author works in this area) which is not found in almost any other textbook. One good thing is this book contains projects at the end of each chapter which will be useful to students.

2) Straumann, Norbert (2012). General Relativity (2nd ed.). Springer.

This is more rigorous than Padmanabhan. It doesn’t discuss QFT in Curved Spacetime.

3) Weinberg, Steven (1972). Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. John Wiley & Sons, Inc.

It is a good book with some problems (not practice problems, which are not there). It doesn’t discuss black holes. Weinberg does not do justice for the geometric approach. Also, the cosmology is outdated.

General relativity advanced books

1) Wald, Robert (1984). General Relativity.

This book is very rigorous. It discusses QFT in Curved Spacetime. The cosmology part is now outdated. It discusses things like proof of Singularity Theorems which are not covered in most of the above books.

2) Poisson, Eric (2004).A RELATIVIST’S TOOLKIT The Mathematics of Black-Hole Mechanics. Cambridge University Press.

It is a very short textbook so explanations won’t be good. It also doesn’t discuss anything related to cosmology and QFT in Curved Spacetime. It mostly deals with the formulation of GR and Black holes.

3) HAWKING and ELLIS (1973). The large scale structure of space-time. CAMBRIDGE MONOGRAPHS ON MATHEMATICAL PHYSICS.

It is slightly more rigorous than Wald. It doesn’t discuss QFT in Curved Spacetime (Hawking and Ellis wrote this before Hawking found the Hawking radiation).

Historically influential books

1) Einstein, Albert (1955). The meaning of relativity: including the relativistic theory of the non-symmetric field. Princeton: Princeton University Press. ISBN 9780691080079. OCLC 177301011.

This book is easy to understand and is written by the man who formulated SR & GR.

2) Misner; Thorne and Wheeler(MTW) (1973). Gravitation. W. H. Freeman Princeton University Press.

A very big book. It was a standard textbook some decades back.

Honourable mentions

1) Chandrasekhar, Subrahmanyan. (1998). The Mathematical Theory of Black Holes. New York: Oxford University Press. ISBN 978-0-19-850370-5.

2) Roger Penrose & Wolfgang Rindler (1987,1988). Spinors and Space-Time: Volume 1 & 2.