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Volume I presents the introductory problems for undergraduate and advanced undergraduate students. In Volume II, the more advanced problems together with their detailed solutions are collected, to meet the needs of graduate students and researchers. Problems included cover most of the new fields in theoretical and mathematical physics such as Lax representation, Backlund transformation, soliton equations, Lie algebra valued differential forms, Hirota technique, Painleve test, the Bethe ansatz, the Yang-Baxter relation, chaos and fractals.