In this dissertation, five new design schemes for achieving the simultaneous noise and input power matching with unconditional stability for monolithic microwave LNA``s are proposed. Two different approaches are adopted, which are the parallel feedback approach and the series feedback approach. In the parallel feedback approach, three new schemes are proposed, which are the cascode resistive parallel feedback (CCPF), and the common-gate inductive parallel feedback (CGPF), and the cascode resistive parallel feedback with local inductive parallel feedback (CCPF+CGPF). In the series feedback approach, two new schemes are proposed. The first one is the cascode inductive seri, five newly proposed schemes have been extensively compared with each other at microwave frequencies. At L-band, CCSF and CSSL+CGPF seem to be the best choice when $0.5 \mu m$ MESFET is used while the CCPF seems to be the best one for L-band application using silicon npn BJT. At C- and X-bands, the topology which has the best noise measure performance with the simultaneous noise and input power matching and unconditional stability at 6 and 12 GHz is CGPF. Other than CGPF, the CSSL+CGPF seems to be the best at 6 GHz, and both CCPF+CGPF and CSSL+CGPF are recommended at 12 GHz. Finally, the newly proposed schemes have been experimentally verified by fabricating several MMIC LNAs using GaAs MESFET technology. The measured responses of the fabricated LNA chips agree well with the simulated performances, which experimentally verifies the newly proposed schemes as well as the design approach of the simultaneous noise and input power matching.