The current thinking, captured in the so-called "Standard Model" of matter, accepts two categories of fundamental building blocks: quarks (six types) and leptons (six types, three of which are neutrinos). In addition, the "mortar" holding these building blocks together, and governing the interactions between them, is a third group of six fundamental particles (the term "particle" starts to be used very loosely at this point), called "force carriers". For example, the familiar photon is a carrier of the electromagnetic force.
If you think it's a bit paradoxical to have have 3 categories of "fundamental particles" containing a total of 18 known varieties, you are quite correct. The Standard Model represents only the current state of knowledge, and a Nobel Prize awaits those who succeed in venturing further.
To get you started on this path, an excellent introduction to the vast realms of Inner Space is the website Particle Adventure created by Lawrence Berkeley National Laboratory.
making a small donation to science.ca.