FREE ONLINE NOTES:Gathmann - "Algebraic Geometry" (All versions are found here. The latest is of 2019.) Just amazing notes; short but very complete, dealing even with schemes and cohomology and proving Riemann-Roch and even hinting Hirzebruch-R-R. It is the best free course in my opinion, to get enough algebraic geometry background to understand the other more advanced and abstract titles. For an abstract algebraic approach, the nice, long notes by Ravi Vakil is found here. (A link to all versions; the latest is of 2017.)
Next to the classics, there is Introduction to algebraic varieties and Introduction to Schemes (available here) by Ellingsrud-Ottem. They are the lecture notes, respectively, for the courses Algebraic Geometry I and II taught at the University of Oslo.
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