In the Molecular Communication (MC), molecules are utilized to encode, transmit, and receive information. Transmission of the information is achieved by means of diffusion of molecules and the information is recovered based on the molecule concentration variations at the receiver location. The MC is very prone to intersymbol interference (ISI) due to residual molecules emitted previously. Furthermore, the stochastic nature of the molecule movements adds noise to the MC. For the first time, we propose four methods for a receiver in the MC to recover the transmitted information distorted by both ISI and noise. We introduce sequence detection methods based on maximum a posteriori (MAP) and maximum likelihood (ML) criterions, a linear equalizer based on minimum mean-square error (MMSE) criterion, and a decision-feedback equalizer (DFE) which is a nonlinear equalizer. We present a channel estimator to estimate time varying MC channel at the receiver. The performances of the proposed methods based on bit error rates are evaluated. The sequence detection methods reveal the best performance at the expense of computational complexity. However, the MMSE equalizer has the lowest performance with the lowest computational complexity. The results show that using these methods significantly increases the information transmission rate in the MC.