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This is, at least, how it went for me just now:

Read:                Think:

field                Q(sqrt 2), or some other number field
finite group         symmetric group
Lie group            the torus R^2/Z^2
ring                 a matrix ring over... some other ring
commutative ring     a polynomial ring k[x_1,...,x__n]x_n]
Lie algebra          sl(2)

This is, at least, how it went for me just now:

Read:                Think:

field                Q(sqrt 2), or some other number field
finite group         symmetric group
Lie group            the torus R^2/Z^2
ring                 a matrix ring over... some other ring
commutative ring     a polynomial ring k[x_1,...,x__n]
Lie algebra          sl(2)

This is, at least, how it went for me just now:

Read:                Think:

field                Q(sqrt 2), or some other number field
finite group         symmetric group
Lie group            the torus R^2/Z^2
ring                 a matrix ring over... some other ring
commutative ring     a polynomial ring k[x_1,...,x_n]
Lie algebra          sl(2)
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Source Link

This is, at least, how it went for me just now:

Read:                Think:

field                Q(sqrt 2), or some other number field
finite group         symmetric group
Lie group            the torus R^2/Z^2
ring                 a matrix ring over... some other ring
commutative ring     a polynomial ring k[x_1,...,x__n]
Lie algebra          sl(2)