Nielson and Chuang, while getting quite dated now [1], is still the best introduction to the conceptual framework of quantum computation and information. Its algorithms section though is not very detailed, and I found it difficult to teach my undergrad students from it.

The qiskit book gives a nice introduction to the algorithms, and contains all the latest algorithms, for someone wanting to learn the field.

[1] it doesn't include a lot of new advances in the past twenty years.