Abstarct: In analogy to cyclic codes, we study linear codes over finite fields obtained from left ideals in a quotient ring of a (non-commutative) skew polynomial ring. The results in this thesis show how existence and properties of such codes are lixnked to arithmetic properties of skew polynomials. This class of codes is a generalization of the θ-cyclic codes are discussed earlier in the literature. However, θ-cyclic codes are powerful representatives of this family and we show that the dual of a θ-cyclic code is still θ-cyclic. Using Groenber baxses, we compute all Euclidean and Hermitian self-dual θ-cyclic codes over F4 of length less than 40, including a [36, 18, 11] Euclidean self-dual θ-cyclic code which improves the previously best known self-dual code of length 36 over F4.