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This article presets a review of lattice lattice basis reduction types. Papercontains the main five types of lattice basis reduction: size reduced (weakHermit), c-reduced, Lovasz condition, Hermit-Korkin-Zolotarev, Minkowskireduced. The article provides references to applications in: information theory(decoding of coding group in MIMO), calculus (minimize of the positivequadratic form), complexity theory and cryptanalysis of Merkle-Hellmancryptography (solving subset sum problems), algebra and control theory(solvingsystem of linear diophantine equation), compiler theory (lattice based memoryallocation), synthesize cryptographic and cryptanalysis in lattice basedcryptography.

Short review of lattice basis reduction types and his applications (Russian)