The question appears to be concerned with establishing an understanding of dependency grammar (DG). DG is indeed increasingly being used in NLP circles as the most workable approach to syntactic structures -- dependency syntax is quite simple compared to constituency syntax. However, introductory textbooks that approach the theory of syntax primarily from a DG perspective are rare. There are at least two exceptions, though:
Matthews, Peter. 1981. Syntax. Cambridge University Press.
van Valin, Robert. 2001. An Introduction to Syntax. Cambrdige University Press.
Matthews' syntax is primarily dependency-based, and van Valin's book devotes a chapter to DG.
A large majority of textbooks on syntax ignore DG entirely, however. My interpretation of this situation is that developments in computational linguistics are out in front of theoretical syntax. Theoretical syntacticians are entrenched in a constituency-based view of syntactic structures, whereas the computational people have to make syntax work for their computational goals, and dependency is more workable in this regard.
The question is asking for sources about DG, though. There are a number of non-introductory texts on theoretical DG, but many of them are not so accessible. However, I think the following text, although dated, is relatively easy to understand:
Schubert, Klaus. 1987. Metataxis: Contrastive Dependency Syntax for Machine Translation.
If one is willing to invest some time in a more comprehensive dependency-based approach to the syntax of natural language, then Richard Hudson's works would be good:
Hudson, Richard. 2007. Language Networks: The New Word Grammar. Oxford University Press.
Hudson, Ricahrd. 2010. An Introduction to Word Grammar. Cambridge University Press.
And if one is particularly willing to invest time and energy in establishing a solid base in DG and its use for computational goals, then this conference would allow one to connect to the international DG community: