The matrix sine-Gordon theory, a matrix generalization of the well-known sine-Gordon theory, is studied. In particular, the A3-generalization where fields take value in SU(2) describes integrable deformations of conformal field theory corresponding to the coset SU(2)× SU(2)/SU(2). Various classical aspects of the matrix sine-Gordon theory are addressed. We find exact solutions, solitons and bre...