Photosystem I (PSI) is a natural light-harvesting complex that contains ~300 chlorophyll molecules (Chls) and drives oxygenic photosynthesis with near-unity quantum efficiency. Understanding the ultrafast photoinduced processes of PSI can help researchers design artificial solar energy conversion devices. However, it is difficult to determine the mechanism of the excitation energy transfer and electron transfer in PSI due to severe spectral congestion and overlapping timescales of ultrafast temporal processes. In this thesis, I use three main experimental and theoretical methods to investigate the ultrafast kinetics and the function of different types of Chls within PSI complexes. 1) I applied ultrafast two-dimensional electronic spectroscopy (2DES) to wild-type and mutant PSI complexes, where mutations were made to Red Chl, Bulk Chl, and reaction center (RC) Chls. 2) I expanded the lifetime-density analysis (LDA) method to be readily applied to two-dimensional spectra. The newly developed 2D-LDA method separates the kinetics associated with the energy-trapping process of the Bulk Chl and Red Chl. 3) I also used numerical and structure-based models to benchmark the 2D-LDA and two-dimensional global lifetime analysis (2D-GLA) methods.The EET network in PSI contains hundreds of Chls with different local environments. The function of each Chl pool can be investigated in wild-type and mutant PSI complexes where the mutations are made near specific Chls. With the help of 2D-LDA, 2D-GLA, and structure-based models, I interpreted the 2DES of wild-type and mutant PSI complexes and constructed a Jablonski diagram to describe the connection between Red Chls, Bulk Chls, and RC Chls of PSI. 1) I found that the energy-trapping kinetics in Red Chl mutants depend on the location of Red Chl pools in PSI. This indicates that the peripheral Red Chl pools are the rate-limiting step in the trapping process. 2) I also investigated two types of antenna Chl mutants: linker Chl mutants and Bulk Chl mutants. My results show that the EET network in PSI contains multiple antenna channels and is robust to minor mutations. 3) I further applied 2DES on the RC mutants, which shows that the EET kinetics of the RC mutants are the same as the wild-type PSI. Meanwhile, the quantum yield of the charge-separated state decreases in the RC mutants and depends on the mutation, indicating that the electron transfer process in the RC is asymmetric. Overall, the information I gathered from my 2DES studies on PSI complexes has provided additional information that can be used to refine structure-based models of PSI complexes and light-harvesting complexes in general.