High-power fiber laser systems enjoy a widespread use in manufacturing, medical, and defense applications as well as scientific research, due to their remarkable power scalability, high electrical to optical efficiency, compactness and ruggedness. However, single-mode fiber power scaling has stagnated in the past years, primarily due to the onset of nonlinear effects such as stimulated Brillouin/Raman scattering and transverse modal instabilities. This thesis addresses the analysis and mitigation of transverse modal instabilities in high-power fiber amplifiers. I describe the high-power fiber amplifier testbed that I set up to test fibers fabricated in house. I will show our results of a Yb-doped fiber amplifier with more than 2.2 kW signal power and beam quality of 1.1 M2. In consequence, I demonstrate mode-selective amplification in a large mode-area Yb-doped fiber using a 3-mode photonic lantern. All three modes were amplified to above 4 W with OSNRs higher than 16 dB. In addition, I show a novel high-speed beam analysis technique to study transverse modal instabilities. To guide fiber designs, I developed a GPU accelerated simulation suite to study the dynamics that occur in high-power fiber amplifiers. A 64 x 64 spatial grid, with 6000 time- and 20000 distance-steps can be solved at 2 min/meter on a GeForce GTX 1080 Ti. Based on these simulations, I will show dynamic transverse modal instability mitigation strategies that rely on mode modulation
