Hmmm, my math got distorted in the previous comment. Also, I should have typed $(H,X_+, X_-)$. This kind of notation has been fairly popular with physicists but also occurs in Bourbaki.

Following Lie and Killing, Elie Cartan (father of Henri) laid foundations for Lie groups and "infinitesimal" groups (later Lie algebras): Paris thesis 1894, etc. Killing studied "Cartan" subalgebras first but didn't invent the "Killing" form. Even in Bourbaki, notation varies: $(H, X_+, X_1), (X,Y,H), (x,h,y)$. Jacobson-Morozov comes from separate work (Duke J. 1938?, Doklady note 1942): see Jacobson (1962 book) pp. 98-100, where $(x,h,y)$ is used. Upper case is common for Lie algebra elements viewed as vector fields or as matrices. Lots of obscure history, but does it matter?

In really ancient times there was handwriting. Then typewriters and carbon paper. The IBM Selectric typewriter had removable key balls, allowing substitution of common math symbols. Otherwise the symbols got inserted afterwards by hand. For typescripts to be typeset, there were conventions about fonts (greek, etc.) involving for instance underlines by colored pencils. This bypassed clumsy handwritten insertions. And then people like Jim Milgram invented pre-TeX word processors for math.

In the U.S. market, Amazon lists the hardcover Birkhauser edition at $29.50 (with free shipping). Apparently Springer/Birkhauser haven't kept it in print. Decades ago I wrote a short review of the book for a specialized journal which I was confident Weil wouldn't read.

The article itself is archived by JSTOR, which means it is freely available to many but not all university users: Hyman Bass, American Journal of Mathematics, Vol. 96, No. 1 (1974), pp. 156-206. The slightly earlier book by Dieudonne in French may not be easily found in libraries, but it treats these groups over fields efficiently.

To expand Wilberd's comment, the ongoing work of R. Bezrukavnikov and I. Mirkovic (following up their joint work with D. Rumynin) takes a more geometric viewpoint. This preprint, now in version 3, addresses the closely related conjectures of Lusztig in 1997-99 on bases in equivariant K-theory: front.math.ucdavis.edu/1001.2562 As in AJS, applications to characteristic $p$ are (so far) dependent on $p$ being "large enough". But the conjectures go beyond restricted Lie algebra representations to those attached to arbitrary nilpotent orbits.

I concur with Wilberd's "presumably", since this large book by Hahn and O'Meara takes real work to get into due to its treatment of classical groups over very general rings. The slender earlier survey by Dieudonne on classical groups does not use algebraic groups or algebraic geometry. But his concise treatment in II.10 (2nd edition) is an alternative for fields of characteristic 2: see MR0310083 (46 #9186) Dieudonne, Jean A., La geometrie des groupes classiques.Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 5. Springer-Verlag, Berlin-New York, 1971.

More context and motivation would help here. You are probably far away from the original motivation of both Shapovalov and Jantzen: find a nonzero symmetric bilinear form on a highest weight module for a semisimple Lie algebra so distinct weight spaces are orthogonal and the radical of the form is the unique maximal submodule. Thus the form is nondegenerate on the simple quotient module. Jantzen worked over the integers in order to study the behavior of f.d. "Weyl modules" mod $p$. Both of them found a miraculous determinant formula on each weight space.

There are definitely some people who have studied classical groups over commutative rings including local rings, for example N.A. Vavilov (St. Petersburg) and his collaborators. My impression is that results have been somewhat scattered and fragmentary. There are some connections with algebraic K-theory as well. A creative literature search using MathSciNet might be useful. Generation of the groups has been a standard theme, but I doubt that you will find definitive results on maximal subgroups for your rings.

Demazure's approach is certainly the most useful from the viewpoint of algebraic geometry in characteristic 0, but the related questions in characteristic $p>0$ remain to a large extent open and are natural follow-ups. As George indicates, Jantzen's book provides access to such questions in a unified framework. Andersen got started on his own work partly by exploring how Demazure's set-up might be adapted to characteristic $p$. But a full analogue of Bott's theorem probably requires some creative use of Kazhdan-Lusztig theory for the affine Weyl group.