Linear algebra concerns vector spaces whether finite- or infinite-dimensional. Abstract algebra, or modern algebra, includes linear algebra, along with many other kinds of objects, such as groups, rings, fields, lattices, and so on. In part, it was an attempt to put mathematics on a more rigorous footing.
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Differential equations, Linear Algebra, Abstract Algebra, Real and Complex Analysis, Advanced Calculus, and lots of other fun stuff.
Example: Algebra will show you how quickly the gallon will fill over time. Calculus will show you how quickly the gallon will fill over time while it is also being slowly drained.
linear
It isn't; the algebra 1 and 2 that you get taught in middle or high school is elementary algebra. When (if you want to) you get into more advanced algebra, you can learn linear algebra (matrix algebra) and abstract algebra (which involves sets, operations on sets, groups, and many more concepts), and probably several more types of algebra I've never heard of.
Linear means a straight line.