Part I. Background: 1. Classical categorical structures; 2. Classical operads and multicategories; 3. Notions of monoidal category; Part II. Operads. 4. Generalized operads and multicategories: basics; 5. Example: fc-multicategories; 6. Generalized operads and multicategories: further theory; 7. Opetopes; Part III. n-categories: 8. Globular operads; 9. A definition of weak n-category; 10. Other definitions of weak n-category; Appendices: A. Symmetric structures; B. Coherence for monoidal categories; C. Special Cartesian monads; D. Free multicategories; E. Definitions of trees; F. Free strict n-categories; G. Initial operad-with-contraction.