A Hyperset Approach to Semistructured or Web-like Databases Since 1970, when E.F. Codd introduced the relational approach to databases, Relational Databases have become the mainstream both in database theory and in the industry of database management systems. This is one of the brightest examples of the influence of mathematics and mathematical logic (where relation is also a fundamental concept) on computer practice. Now a new idea of semistructured databases (SSD) has arisen. It does not fit well with the relational approach although it is usually presented in terms of edge labelled graphs which are mathematically just two column relational tables (with labelled rows). The point is that some other kind of issues with such graphs arises which are not so "relational". The Hyperset approach to SSD is intimately connected with the graph approach and is, in fact, a natural generalization of the relational approach. The idea is extremely simple, but abstract. Each vertex X of a graph is considered as a (hyper)set name and generates a set equation X = {l_1:X_1,...,l_n:X_n} where l_i:X -> X_i are all outgoing l_i-labelled edges. According to the (non-wellfounded) Hyperset Theory (from a book of P.Azcel or another book of J. Barwise and L. Moss) each such system of set equations generated by a graph has a unique solution in the universe of (abstract) hypersets. Each hyperset X is a set of labelled sets of sets of sets, etc., possibly with cycles (according to the given graph or system of set equations). Thus, graph vertices only represent hypersets. These are hypersets which are considered as (abstract) SSD states (like relations which are also sets of tuples). Any query to SSD in this approach is just an operation over hypersets (like operations over relations in the relational approach to databases), whereas graphs or, equivalently, systems of set equations representing hypersets and SSDs serve to compute these abstract operations/queries by appropriate (restructuring and bisimulation invariant) graph transformers. A hyperset query language Delta and its more practical version will be discussed whose expressive power proves to be exactly PTIME (also for the case of multi-hypersets). Some variations of Delta for the case of acyclic graphs (sets) have expressive power (N/D)LOGSPACE. No such results are known to the author for purely graph approaches to SSD (without involving hypersets). Any SSD, as a system of hyperset equations, may be divided into parts and represented as, say, HTML files distributed potentially over the world with each set name X_i "clickable" and leading to (either the same or possibly remote) file with the corresponding equation X_i = {...}. This, as well as the arbitrary graph structure of SSD, suggests calling such databases Web-like (WDB). Thus, in principle, the Delta-language can be considered as a powerful, flexible and restructuring (unlike the usual querying mechanisms of, e.g., Google) query language to WDB or even to WWW. Some implementation issues potentially leading to a WDBMS, (like many existing RDBMS) for example, multiple mobile distributed agent execution of Delta queries may be discussed, too. (This talk is based on joint works with my colleagues Alexei Lisitsa, Alexandr Leontjev and Yuri Serdyuk. Also, student Richard Molyneux is currently working on a new attempt of implementation of Delta based on HTML files of the above kind.)