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Similar themes. SICP is a little more academic. You build a compiler, do more math, etc.

PAIP also focuses more on Common Lisp specifics.

Different audiences too. SICP is meant for first year college students with little or no CS or programming experience. PAIP assumes no Common Lisp experience, but it's not an introductory text for CS. It's an introductory text for GOFAI and Common Lisp.

Though, PAIP covers a lot of SICP content, but differently. It also includes implementations of programming languages. PAIP is only partly an introductory text to Common Lisp, it's more about actual software design and development with Common Lisp.

IMHO PAIP is extremely well written. Book and Code: https://github.com/norvig/paip-lisp

SICP has a mixed reception. Many find it excellent, others find it to focused to teach CS concepts in a math-oriented way. Thus there have been written several alternatives to SICP, using Scheme, Logo, other Functional Programming Languages, ... I think it's a great book, with a lot of excellent books written as a reaction to it.

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