Let \(M = (M, g, \varphi, \xi,\eta)\) be an almost contact Riemannian manifold. Then \(M\) is said to be almost contact homogeneous if it admits a transitive Lie group of isometries leaving \(\varphi\) invariant. On such a manifold there exists an almost contact homogeneous structure, i.e., a (1,2)-tensor field \(T\) such that with \(\overline {\nabla} = \nabla - T\) we have \(\overline {\nabla} R = \overline {\nabla} T = \overline {\nabla} g = \overline {\nabla} \varphi = 0\) where \(\nabla\) denotes the Levi Civita connection and \(R\) the Riemannian curvature tensor of \((M,g)\). Conversely, any connected, simply connected, complete \(M\) which admits such a structure is an almost contact homogeneous space. The author classifies these structures into different classes by using representation theory. To do this, she considers the vector space \({\mathcal T} (V)\) of (0,3)- tensors over the real vector space \(V(\langle\;,\;\rangle, \varphi, \xi, \eta)\) of dimension \(2n + 1\), having the same algebraic symmetries as the almost contact homogeneous structures (in their (0,3)-version) and determines a complete decomposition of \({\mathcal T} (V)\) into eighteen irreducible invariant subspaces under the natural action of \({\mathcal U}(n) \times 1\). This decomposition is not unique. She also derives a second decomposition and discusses it in relation with the one obtained by Padron, Chinea and González and used to classify almost contact manifolds.