Samuel Rathmanner and Marcus Hutter, "A Philosophical Treatise of Universal Induction"
in Entropy 2011, 13, 1076-1136. A very clear philosophical and mathematical analysis of Solomonoff's Theory of Inductive Inference.
Grace Solomonoff, "Events Foreseen", biography of Ray and Description of his Theory of Probability and Prediction, expanded from the biography in Melbourne Proceedings (Springer Pub.)
An article about Algorithmic Probability is in the
Wikipedia .
For another detailed description of Algorithmic Probability, see "Algorithmic Probability"
by Marcus Hutter, Shane Legg, and Paul Vitanyi, in the Scholarpedia,(8):2572.
Peter Gacs and Paul Vitanyi, IEEE In Memoriam
gives an excellent discussion of Ray's work, with a detailed description of Solomonoff's General Theory of Inductive inference.
Filip Dolegiewicz, The Importance of Ray Solomonoff's
"An Inductive Inference Machine",
A short film giving an excellent brief overview of "An Inductive Inference Machine"
Solomonoff's 1956 Dartmouth paper on machine learning,
and then describing his development of Algorithmic Probability.
An article about the General Theory of Inductive Inference, and some of the variants by others is in the
Wikipedia ; parts of this article, however are very uneven
For a detailed description of Algorithmic Information Theory, see Algorithmic Information Theory, by Marcus Hutter,
in the Scholarpedia, 2(3):2519.