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Derek Raine and Ted Thomas
An introduction to the science of cosmology
The last part of the book applies such models to the real universe, and in particular its early stages. Thus there is a description the Hot Big Bang, with the origin of elementary particles, followed by a chapter on the theory of inflation. the book ends with a look at the evolution of large scale structure in the universe.
Naturally a textbook such as this needs the reader to have some mathematical experience, but if you know a bit about differential equations then this won't be a challenge, and the first part of the book needs less mathematics. The book has problems set at the end of each chapter, and looks suitalbe for those wishing to learn cosmology in independent study. It's a short book, but I feel that anyone who has followed it will be well placed to understand much current cosmological research.