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In this research, we have captured, in pattern form, key elements of programming and design in four programming paradigms (imperative, object-oriented, functional and logical) as well as multiparadigm programming. These pattern sets have formed a foundation upon which we were able to build a deeper understanding of multiparadigm programming and design. For each paradigm, we identified sets of programming patterns. We then identified design patterns for those paradigms that already have design methodologies (imperative and object-oriented). For those that do not (functional and logical), we created design pattern sets that may yet play a seminal role in formal design methodologies for those paradigms. From the relationships between programming and design patterns, we were able to identify and record methodological patterns that provide generative mappings between programming patterns and design patterns. From the sets of programming patterns, we were able to derive a pattern set for multiparadigm programming. We were also able to perform a critical analysis of the multiparadigm programming language Leda using this pattern set. Finally, we were able to apply the methodological patterns to this multiparadigm programming pattern set to aid in our search for multiparadigm design patterns. We were also able to derive insight into multiparadigm design patterns by studying the pattern sets for each of the four paradigms studied. Armed with this rich pattern system, we then created and presented a new pattern-based methodology for multiparadigm design. Finally, we applied our methodology and our pattern sets to three common design problems. We found that this new methodology lent new insights into software design, and suggested the role that multiparadigm programming and design can play in many aspects of software creation.