In [21] and [22], the authors proposed hybrid precoding designs based on Euclidean distance minimization between the hybrid beamforming solution and the optimal beamformer. The authors of [23; 24; 25] proposed codebook-based hybrid transceiver designs, where the analog beamformers were selected from the pre-defined candidate vectors. The common examples of these pre-arranged candidates are beam-steering vectors and discrete Fourier transform (DFT) beamformers. Hybrid beamforming algorithms in [26; 27; 28] are based on the minimum mean squared error (MMSE) criterion for deriving the hybrid beamforming matrices. In contrast to the fully-connected structure, the authors of [29; 30; 31] proposed partially-connected architectures for hybrid beamforming which is done to obtain the energy efficient solution with relatively low hardware complexity. This structure allows the connection of each RF chain to a fixed non-overlapping subset of the antennas while deriving the analog RF beamformer corresponding to this antenna sub-array. In particular, hybrid beamforming schemes with partially-connected architecture may not always achieve satisfactory performance [32; 33] for the following reasons: (1) it is difficult to have fine control over the beam and this tendency leads to the less accurate beamforming; (2) the underlying structure limits the flexibility of large antenna arrays and causes significant degradation in performance. In [34], orthogonal matching pursuit (OMP) based solution proposed in [23] was extended to design the relay-assisted MIMO network with AF relaying protocol. The hybrid transceiver design proposed in [23] was further modified in [35] and [36] to design multi-relay MIMO systems. In [35], only the analog precoders/combiners were employed at relay nodes, while hybrid processing components were used at source and destination. In contrast to the hybrid precoding design in [35], the proposed algorithm in [36] used hybrid beamformers at all communicating nodes. In [37], the digital baseband processing component and the analog RF beamformer were designed separately for a single relay multi-user MIMO system by using pre-defined codebooks, and this approach was adopted to avoid intractable searching problem. The authors of [38] proposed the hybrid beamforming scheme as a matrix factorization problem, where the alternating direction method of multipliers (ADMM) was exploited to design the analog RF and digital baseband processing components. This method does not require any pre-defined codebook for the selection of best beamforming vectors. The authors of [39] introduced the notion of deep neural network for training the hybrid precoder and combiner; the hybrid precoding solution achieved relatively superior performance when compared with the existing hybrid beamforming algorithms. Deep learning framework shifts the run-time computational complexity for designing the hybrid beamformers to the off-line training process. Contrary to the aforementioned works on relay-assisted hybrid beamforming for different communication networks (e.g., [34; 35; 36; 37; 38]), this paper proposes a beamforming and relay selection simultaneously. Relay selection in a multi-hop transmission system is an essential design aspect to avoid performance degradation due to error propagation [40; 41]. Therefore, the primary focus of present research work is to design a hybrid beamforming solution for a fully-connected multi-relay mm-Wave MIMO network with a relay selection that may enable to maximize the achievable rate. This target can be achieved by maximizing end-to-end SNR, which is a better choice as it is directly related to capacity expression [42]. In this regard, the original complicated optimization problem is decomposed into two independent SNR maximization problems. Then, a decoupled approach is considered which allows to design the analog RF precoders/combiners and the corresponding baseband processing components separately.