© 2015 AIP Publishing LLC. Nonlinear two-dimensional Fourier transform (2DFT) and linear absorption spectroscopy are used to study the electronic structure and optical properties of excitons in the layered semiconductor GaSe. At the 1s exciton resonance, two peaks are identified in the absorption spectra, which are assigned to splitting of the exciton ground state into the triplet and singlet states. 2DFT spectra acquired for co-linear polarization of the excitation pulses feature an additional peak originating from coherent energy transfer between the singlet and triplet. At cross-linear polarization of the excitation pulses, the 2DFT spectra expose a new peak likely originating from bound biexcitons. The polarization dependent 2DFT spectra are well reproduced by simulations using the optical Bloch equations for a four level system, where many-body effects are included phenomenologically. Although biexciton effects are thought to be strong in this material, only moderate contributions from bound biexciton creation can be observed. The biexciton binding energy of ∼2 meV was estimated from the separation of the peaks in the 2DFT spectra. Temperature dependent absorption and 2DFT measurements, combined with "ab initio" theoretical calculations of the phonon spectra, indicate strong interaction with the A 1 ′ phonon mode. Excitation density dependent 2DFT measurements reveal excitation induced dephasing and provide a lower limit for the homogeneous linewidth of the excitons in the present GaSe crystal.