Abstract: This thesis presents the results of low temperature transport experiments in high mobility two-dimensional electron systems (2DESs) realized in Si/SiGe heterostructures. By applying an external magnetic (B) field, fundamental 2D electron physics in Si has been studied in different regimes of interest. At zero perpendicular B-field, the apparent 2D metal-insulator transition (MIT) and the existence of a metallic-like ground state are currently under hot debates. Our gated Si sample shows the 2D MIT at a critical density n_c = 0.32 × 1011cm-2, much lower than the n_c = 0.8 × 10 11cm-2 observed in the so-called clean Si-MOSFETs, suggesting that n_c decreases with increasing sample quality. The in-plane magnetoresistance (MR) measurements were also performed and the results show qualitative differences from the observations in Si-MOSFETs. In the integer quantum Hall effect (IQHE) regime, the energy of the two out-of-plane valleys in Si differs by a small valley splitting (Δ _v), which is associated with the odd-integer states. Our tilted field magnetotransport measurements show that, even at the same filling factor, Δ _v is significantly different when the Landau level (LL) and spin indices are changed. Many-body effect such as screening of the Coulomb interaction has to be taken into account to understand this phenomenon. More surprisingly, in the coincidence region where energy levels cross each other, the inter-valley gap rises toward the coincidence angle. Analysis based on level anti-crossing or quantum Hall ferromagnetism does not explain such phenomenon and correlations between opposite spins and/or valleys may be responsible for this anomaly. The valley degree of freedom in Si also plays a vital role in the regime of fractional quantum Hall effect (FQHE), where the single-particle kinetic energy of electrons is degenerate and interaction effects dominate. In our experiment, the two-flux composite Fermion (CF) series of the principal FQHE states is observed around ν = 1/2. In contrast to the observations in single-valley systems, the ν = 3/5 state is weaker than the nearby ν = 4/7 state and the ν = 3/7 state is conspicuously missing, resembling the observation in the IQHE regime that ν = 3 is weaker than the nearby ν = 4 state. We show that this phenomenon can be quantitatively understood given that the CFs assume their own valley degeneracy.