the original red book, issued in a second edition, were notes for a course by Mumford introducing the ideas of schemes, beginning with a brief sketch first of more classical "varieties". Then he discusses basic concepts of scheme theory, with motivation for taking a categorical perspective for instance in defining products. One usually thinks of a product of X and Y as a set of ordered pairs of elements (x,y), but this fails for schemes because the "points" are more sophisticated, and can have various dimensions, i.e. not all points in a scheme are zero dimensional. So the right approach is to realize that a product of X and Y is another object Z equipped with "projection" maps Z-->X and Z-->Y such that every pair of maps A-->X and A-->Y is induced from a unique map A-->Z via the projections. Then he discusses the consequences and complications arising from changing the ring of scalars, not just doing geometry over R or over C, and how that introduces Galois theoretic matters and leads to a concept of a variety as a "functor". Then he discusses the local theory and how to algebraicize matters via consideration of coherent and quasi coherent modules, somewhat analogous to vector bundles in differential geometry. Finally he discusses some classical results of Zariski, such as the "main thorem" describing the geometry of "normal" varieties.
The later version (AG II?), edited by Oda, omits the discussion of classical varieties and begins as I recall with affine schemes. (Affine schemes are to schemes as coordinate neighborhoods are to manifolds.) He also includes some more sophisticated versions of his discussion of complex geometry as introduced in his Algebraic varieties I. Finally he discusses in some detail the main topic omitted from the red book, namely sheaf cohomology, especially in the case of the Cech construction, including a discussion of spectral sequences, for which he tries to "debunk" their reputation for being so difficult.
The little volume Alg Var I, is a very terse and jam packed volume on complex algebraic geometry in projective space with many useful results proved carefully but succinctly that are often omitted in other books. He distills there a proof of desingularization of curves from the monumental argument by Hironaka for the general n dimensional variety, and he gives a complete proof that every non singular cubic surface has exactly 27 lines on it. This is a concise and deep treatment of many classical topics, including a very clear and useful account of the classical Riemann Roch theorem for curves.
So the books are logically ordered as : 1) AGI, 2) redbook, 3) AGII (Oda), but I would not completely postpone reading the later volumes if they are your interest, since you could conceivably spend years just mastering the first one. I believe you can reasonably begin on either of the first two, but it seems more challenging to begin with the third.
By the way, many people feel the best beginning book on algebraic geometry is the book of Shafarevich, but it is not primarily aimed at Grothendieck's theory.
(sorry, I have no easy way to send copies of the maryland notes, but they should exist in libraries.)
there is another source for an intro to grothendieck style AG, a translation of three volumes from the Japanese, namely AG 1, 2 and 3, by Kenji Ueno. Japanese works tend to be rather complete, e.g. there are solutions to exercises given. This work covers transition from varieties to schemes, schemes, and cohomology.
https://www.amazon.com/s/ref=nb_sb_noss?url=search-alias=stripbooks&field-keywords=kenji+ueno,+algebraic+geometry
edit: I tried reading a few pages in vol. 1 of this series just now and was not favorably impressed. The style seems to emphasize complicated and unilluminating formulas, as opposed to clear insights, and the formulas I just checked (p.31) even seem to be somewhat in error, (notice on line -14, p.31, that n+1 quantities have been substituted into a polynomial f of only n variables - the term x^(k),j+1/x^(k),j+1 should have been omitted), as is apparently also the summary of their meaning at the bottom of page; i.e. I believe one does not replace xi/xj by xi/xk, but rather by (xi/xk)/(xj/xk), as is visible in the line -14 just referred to. Otherwise the substitution would not make sense, as the corresponding functions would not be equal. The substitution is supposed to make different representations of the same function correspond to each other. Still I am sure there are many things to be learned from this source, e.g. in the form of explicit details. E.g. the discussion of existence of fibre products on pages 120-127 of Ueno's book seems more detailed than the sketch on pages 84-85 in Mumford's red book.
further edit: I just tried to read even the introductory parts of that treatment of fibre products, the discussion of representable functors, and found it also very confusing, due again to an apparent lack of facility in the use of the English language by the translator. Again the formulas are mostly correct, with a few typos, but the discussion surrounding their meaning is quite confusing, i.e. these formulas do not seem to be showing what he says they are. Or rather it takes some familiarity with what is going on to understand just what the brief choice of words is meant to convey. So unless one already knows what is going on, it is hard to find out from the text. This is too bad, as Ueno is a world renowned expert.
So I cannot recommend the English translation of Ueno's book to a beginner, although very likely Japanese readers with access to the Japanese original will no doubt have a completely different experience.
Actually, having struggled to figure out what was meant by the explanations in Ueno, and having corrected the typos, I appreciate the beauty of this section on representable functors more. The mathematics is well chosen, and details are provided for some helpful parts, and the occasional remark as to the importance of a topic is helpful. I have actually learned something. But it is probably crucial that I already knew what was going on. And I am clearly being unfair and ungrateful to the translator, since with effort I can learn from his translation, whereas the original would be impenetrable to me.
Unfortunately such minor but troublesome errors are often introduced when a work is translated from another language. Of course it is also true that many typographical errors were introduced into Mumford's red book as well, when it was re-typeset by Springer, so the original notes from Harvard's math department are preferable, but now quite rare. (I bought mine there over 50 years ago, but also have the Springer version which I am actually reading now. A bonus of the Springer version, at least the second expanded edition, is that it includes the wonderful 1974 lectures on Curves and their Jacobians, delivered by Mumford at Univ. of Michigan.) Another advantage of the original redbook is the more generous spacing of the type on the page, which clues you in as to when a new idea is being begun. This is often obscured in the more crowded Springer formatting.
So my advice, for an introduction to Grothendieck's ideas, is to begin with Mumford's red book, consulting other books for details. Then progress to Hartshorne. But if you are attracted to the task of reading Grothendieck-Dieudonne' (it really is a joint work, probably largely written by Dieudonne'), keep a copy of EGA or SGA handy and try reading it from time to time. Or read Hartshorne and use EGA to fill details. I myself am still plowing through Mumford's redbook, after more than 2 years, off and on, and it is to me at least, not at all easy sailing. Still it is wonderfully eye-opening, but every line requires thought, and sometimes outside study. This why I was led to try Ueno for more detail on fiber products, but may now turn instead to Hartshorne, or maybe back to Ueno, since I do roughly know what is the point of it. So I need about as long to figure out what Ueno's book is trying to say as I do to understand what Mumford is not saying. Perhaps oddly, I still prefer a cryptic remark by an expert, to a detailed explanation from a novice, (not thinking of Ueno here, but others, more or less like myself, who have written treatments), which latter may have actually missed the entire point.
The paradox is that a more detailed work is not necessarily easier to read, because it is just too long. as they say, you don't see the forest for the trees.
in the special but important case of curves, there is a fantastic book by George Kempf, explaining and using Grothendieck's ideas to treat Jacobians of curves, called Abelian Integrals, that used to be available from the University of Mexico Autonoma. Some libraries have this as well, but it is not as well known as it deserves to be due probably to being published only by the Univ of Mexico.
https://www.amazon.com/dp/B007FD5XKW/?tag=pfamazon01-20
This is not necessarily easy reading, but provides important material in a form not available elsewhere.
By the way, George Kempf himself is one of my brilliant friends who read EGA. George is also author of an amazingly terse but informative book Algebraic varieties, which treats sheaf cohomology in the context of varieties as opposed to schemes, but which is also subject to numerous typographical errors.
https://www.amazon.com/dp/0521426138/?tag=pfamazon01-20
