This paper consists of three complementary parts. First, there are the fundamental problems and challenges about the foundations [1,2,9] of Machine Composition (MC), especially in relation to human composition. Second, there is the background of existing theory and experimental results from main areas of Machine Compositional Research and their constructions of prototypes [4,5,7]. And finally, the most practical part introduces two important environments or tools [3,6,8] for the construction of machine compositional systems.In the first chapter, a Sudoku algorithm is proposed and put into perspective with regard to musical and computational domains as a model for algorithmic as well as compositional activities. Many similarities are found to exist between the creative activities of computational problem solving and com-”positioning” in music. In the discussion of Bach, Bruckner and Debussy, interpretations of rule system design and expansion, instead of the conventional idea of the artist's “rule-breaking” are proposed as a better model for creativity. Recent computational trends attempt to “soften” programming cultures. A distinction between hard and soft algorithmic activities is proposed that accounts for both the similarities and differences between both activities. In chapter two, the origin of music is placed in the continuum of natural evolution, and this underlines the vital importance of musical learning and social culture. A musical learning cycle is employed to account for both prehistoric music learning and machine learning, and opens up a unified frame for man and machine. The objects that represent the parts of reality in computational as well as musicological domains are discussed and problematized. The many machine/AI paradigms and music systems choose radically different approaches to represent information and sound. The chapter concludes with the proposal of a procedural epistemology, based on pragmatic and empiricist epistemologies, both naturalizing and naturalized themselves, as exemplified in the ontic engineering and design for Machine Composition. In chapter four, five and seven, the various paradigms of Machine Composition and their AI techniques are exhibited and discussed. The improvisational system of Cypher (Rowe) is a typical MC system where many levels and modules of knowledge interrelate to produce a responsive and flexible player paradigm. Cypher is informed by theory and knowledge from the musical domain. In contrast, EMI (Cope), staged in chapter 5, is a typical inductive learning system that extracts style features (signatures) from a sample collection of known composer styles. EMI's Turing-test-like “Game”, where many people are failing to distinguish between machine and man creation, is discussed. In chapter 7, many of the more recent trends of MC are investigated. Especially mathematical and biologically oriented research is given attention. Music generated from fractals or chaos and music derived from evolutionary principles and adapted to synthetic environments are some of the newest methodologies. Todd and Werner's Frankensteinian methods for evolutionary composition are concluding the theoretical part of this paper.In chapter three and six, MAX and Lisp/CommonMusic are introduced and discussed. MAX's graphical and eclectic user interface is contrasted with the very 'general purpose' programming language of CommonLisp. Both approaches have significant relative advantages and disadvantages and seem to work even better in integration. In chapter eight, maxlisp, the embedded version of CLisp for Max/MSP is examined. Using maxlisp, a user may choose to build MAX-patches in various styles of MAX, supported by lisp-objects (maxlisp-objects) doing the rigorous computational tasks. Arguments in favor of integration and hybrid methodologies are endorsed. Finally, chapter nine, sums up some of the encountered notorious problems in and around MC. Questions concerning the classification of MC, questions of sceptical nature in general, interpretations about creativity and originality, as well as philosophical theories about music contribute to the proposal of a tentative framework of a machine compositional aesthetics, compatible with the evolutionary and Darwinistic theories about nature and culture alike.