1. A Brief Introduction to Modular Forms.- 2. Period Polynomials.- 3. Maass Wave Forms of Real Weight.- 4. Families of Maass Cusp Forms, L-Series and Eichler Integrals.- 5. Period Functions.- 6. Continued Fractions and the Transfer Operator Approach.- 7. Weak Harmonic Maass Wave Forms.- A. Background Material.- References.- Symbol Index.- Index.