I.- 1. Introduction.- 2. Conventional Magnetism Diagrams and Their Limitations. Present State of the Art.- 3. Tensor Operator Algebra for Point Groups.- 4. The Weak-Field Method.- 5. The Intermediate-Field Method.- 6. Description of Programs.- 7. Description of the Diagrams and Their Application.- Appendix. The Projection Operators.- References.- II Diagrams.- Average Effective Magnetic Moment as Function of Temperature and Dq, K =1.0.- Average Effective Magnetic Moment as Function of Temperature and Dq, K = 0.75, 0.50.- Principal Effective Magnetic Moments as Function of Temperature and Dq.