General theory on Hash Functions?
There is a general cryptographic theory of provably secure hash functions. There are several inequivalent notions of security. Hash functions are a cryptographic primitive, and the goal of cryptography is to explore relations between different primitives – can one primitive be constructed using the other.

All of this, however, has no relevance on hash functions practically used, for various reasons. Practically, hash functions come in two flavors: cryptographically secure and not cryptographically secure. There isn't really any theory regarding the construction of both types. Cryptographically secure hash functions are constructed according to various and changing heuristic principles, but their strength lies in the community trying to break them and failing. Non-secure hash functions have other properties, and successful one have emerged from practice.

Don't construct your own hash function. If you attempt to construct a cryptographically secure hash function, you will probably fail unless you're an expert. Constructing a non-secure hash function is less harmful, but still, existing ones are probably better than one you would come up with.

If you want a hash function with a particular integer range $[a,b]$ (as indicated in the comments), there are two basic options:


If your function doesn't need to be cryptographically secure, you can use the formula $h \pmod{b-a+1} + a$, where $h$ is a general-purpose hash function. The range of $h$ should be large compared to $b-a+1$, unless $b-a+1$ happens to divide the range of $h$.
If your function does need to be cryptographically secure, you have to be more careful. In that case I suggest you ask a question on the dedicated crypto stackexchange site.