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This book, “The Buddhivilasini: Commentary of Ganesa Daivajna on the Lilavati of Bhäskaracarya II” is a version of the thesis, for which Dr V. Ramakalyani has been awarded the degree of Doctor of Philosophy by the University of Madras in 2018. Among the published commentaries on Lilavati, Buddhivilasini stands out for its characteristic treatment of the original work as Buddhivilasini contains more than hundred upapattis (Indian proofs) for almost all the rules of Lilavati. In the context of Buddhivilasini, upapatti is either a description of the process, numerical demonstration thereof, verbal explanation, reasoning utilising algebraic rules, proportion, examples or justification. This book consists of nine chapters. First chapter introduces the background relating to Indian contribution to mathematics. Second to eighth chapters consist of study of the upapattis on parikarmastakam (eight operations on arithmetic, fractions and zero), prakirnakas (miscellaneous units), misra-vyavahara (investigation of mixed units) sredha-vyavahara (progressions), Ksetra-vyavahara (geometry), Itara-vyavahara dealing with the khata (volume of excavations), citi (stacks), rasi (mound of grains) and chaya (shadows and gnomon), kuttaka (an indeterminate equation of degree one) and ankapasa, dealing with combinatorics. The translation of the passages in Buddhivilasini and explanations in modern notations are given with valuable remarks. Ganesa’s contribution to mathematics, style of commenting and his erudition are discussed in the last chapter. Six appendices, bibliography and index are given at the end. On the whole this is a valuable contribution to the historiography of mathematical literature in Sanskrit.