In this thesis, we presents an expanded account of construction of low-density parity-check(LDPC) codes based on two articles L. Q. Zeng(2008). This thesis presents ten algebraic methods for constructing non-binary low-density parity-check codes based on finite fields and finite geometries. These codes have Tanner graphs with girth at least 6. Simulations show that these codes perform well under iterative decoding algorithms. The parity-check matrices of the codes constructed by finite fields usually have nearly full row rank, hence the encoding complexity is low. In general, the construction methods based on finite fields are suitable for generating high-rate codes, with parity-check matrices having small column weight. The parity-check matrices of the codes constructed by the finite geometrices usually have large column weights, hence these codes may show a very low error floor.