The report covers some of the principles of the mechanics relevant to the description of composite materials. The contents of these notes may provide useful information for the understanding of current publications and reports related to composite materials. Emphasis is placed on the use of indicial notation and operations. The rules governing the use of the contracted notation are also outlined. The generalized Hooke's law and its transformation properties, material symmetries, and engineering constants are also discussed. The plane strain and plane stress problems are discussed in detail. Finally, the elastic moduli of laminated anisotropic materials, and the strength of both unidirectional and laminated composites are covered.