M.S. Level Material
Advanced Algebra
Groups
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Series of groups (Jordan-Holder Theorem), solvable and nilpotent groups
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Representation theory (Maschke's Theorem)
Rings
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Modules
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Division rings (Wedderburn's Theorem)
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Noetherian rings (Hilbert Basis Theorem, power series rings), localization
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Semi-simple rings (Density Theorem)
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Gröbner Bases
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Affine algebraic varieties
Fields
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Separable, inseparable and purely inseparable extensions, normal extensions
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Transcendental extensions (transcendence bases)
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Galois theory
References
Dummit and Foote: Abstract Algebra
Hungerford: Algebra
Lang: Algebra
Rotman: Advanced Modern Algebra