The paper by Levin and Wen introduces the concept of string-net condensation as a physical mechanism for generating topological phases in quantum systems. They argue that when extended objects, called "string-nets," become highly fluctuating and condense, they can give rise to a wide class of exotic phases. The authors derive exact soluble Hamiltonians for 2D local bosonic models whose ground states are string-net condensed states, corresponding to 2D parity-invariant topological phases. These models reveal the mathematical framework of tensor category theory, which characterizes and classifies topological phases. One of the Hamiltonians, a spin-1/2 system on a honeycomb lattice, is shown to be a theoretical realization of a fault-tolerant quantum computer. In higher dimensions, string-net condensation naturally leads to the emergence of both gauge bosons and fermions, providing a mechanism for unifying these particles in 3D and higher dimensions. The paper also discusses the general string-net picture, including the construction of fixed-point wave functions and Hamiltonians for string-net condensed phases, and the calculation of quasiparticle excitations.The paper by Levin and Wen introduces the concept of string-net condensation as a physical mechanism for generating topological phases in quantum systems. They argue that when extended objects, called "string-nets," become highly fluctuating and condense, they can give rise to a wide class of exotic phases. The authors derive exact soluble Hamiltonians for 2D local bosonic models whose ground states are string-net condensed states, corresponding to 2D parity-invariant topological phases. These models reveal the mathematical framework of tensor category theory, which characterizes and classifies topological phases. One of the Hamiltonians, a spin-1/2 system on a honeycomb lattice, is shown to be a theoretical realization of a fault-tolerant quantum computer. In higher dimensions, string-net condensation naturally leads to the emergence of both gauge bosons and fermions, providing a mechanism for unifying these particles in 3D and higher dimensions. The paper also discusses the general string-net picture, including the construction of fixed-point wave functions and Hamiltonians for string-net condensed phases, and the calculation of quasiparticle excitations.