Publisher contracts can vary quite a lot, but in the case of traditional book publishing it is common for the publishers to expect the copyright in the work to be assigned to them. Before you accept the agreement it is worth taking a critical look at the details. While the publisher is usually in a more powerful position, you could still try to negotiate if there are aspects which you don’t like.
An alternative would be for you to retain the copyright and grant the other publisher a licence to publish for example, which means that you have not entirely surrendered the Intellectual Property rights in the book. Even if the publisher is amenable to this suggestion, they may still insist upon an all encompassing exclusive licence and a cynic might say there is no practical difference to assigning the copyright.
If copyright is assigned, the publisher may also grant you a licence to make use of your own work in certain ways, such as reproducing extracts on your personal or institutional website. It is always worth pressing the publisher about any specific use of the work you would wish to make. Recently a UCL academic author was concerned that assigning the copyright in his work (as requested) would prevent him from translating and publishing the work in his native language (Portuguese) at a future date. The author was right to be concerned, since copyright includes the right to produce an adapted version, such as a translation. The answer: negotiate on that point with the publisher to see whether they will licence that particular right back to you.