Here are some recommended books to learn the basics of general relativity and cosmology, excluding string theory:
"A First Course in General Relativity" by Bernard F. Schutz: This book provides a comprehensive introduction to general relativity, starting from the basics and gradually building up to more advanced topics. It covers the mathematical foundations, the geometric nature of gravity, and applications in astrophysics and cosmology.
"General Relativity: An Introduction for Physicists" by M. P. Hobson, G. P. Efstathiou, and A. N. Lasenby: This textbook offers a thorough introduction to general relativity, emphasizing its mathematical aspects. It covers tensor calculus, the Einstein field equations, black holes, gravitational waves, and cosmology.
"Spacetime and Geometry: An Introduction to General Relativity" by Sean Carroll: This book provides a clear and accessible introduction to general relativity, focusing on the geometrical aspects of the theory. It covers topics such as curved spacetime, the equivalence principle, gravitational waves, and cosmology.
"Gravity: An Introduction to Einstein's General Relativity" by James B. Hartle: This book offers a conceptual and intuitive introduction to general relativity. It covers the basics of curved spacetime, the principle of equivalence, black holes, and cosmology, emphasizing a deep understanding of the underlying physical concepts.
"Cosmology" by Steven Weinberg: While this book delves into cosmology, it also provides a solid foundation in general relativity. Weinberg, a Nobel laureate, covers topics such as the expansion of the universe, cosmic microwave background radiation, dark matter, and dark energy. It combines theoretical explanations with observational and experimental results.
These books should provide you with a good starting point for understanding general relativity and cosmology. They vary in their level of mathematical rigor and conceptual depth, so you can choose the one that suits your background and interests. Remember that general relativity and cosmology are complex subjects, so be prepared to spend time studying and working through the material to gain a thorough understanding.