Reading material about the special unitary group

There are many sources describing the structure of SU(2), and some sources mention the connection with the Pauli matrices. One such is the book "Essential mathematics for undergraduates. A guided approach to Algebra, Geometry, Topology and Analysis" by Simon G. Chiossi, available as ePUB from Springer. See sections 16.1 (especially example 16.6), 17.1 and 17.2 (especially Example (iv) right after Theorem 17.6). For proofs about the identification of SU(2)/{I, -I} as SO(3) one needs more advanced algebra books, for example M. Artin's "Algebra", 2nd edition, Prentice Hall 2011 (see section 9.3).