1. The wave equation with examples from mechanics, optics, electromagnetism and quantum mechanics 2. Waves in general relativity, quantum gravity, plasma physics and quantum stochastics 3. Analysis of waves in engineering and optical systems, in biological systems, classical and in quantum blackhole physics 4. Probability Theory and Statistics required for random wave motion analysis 5. An introduction to probability and random processes in circuit and field theory from a pedagogical viewpoint 6. Applications of Lie groups and Lie algebras, filtering, field quantization, numerical methods for quantum mechanical problems.