Superconductors and superfluids have ever since their discovery been of great academic interest in physics. This is reflected by the fact that twenty people have been awarded Nobel prizes for studying such systems during the last century, yet the most outstanding problems in the field remain open. The current proposal (i) confronts outstanding open questions in superconductivity and (ii) focuses on predicting a new type of superconducting and superfluid behavior. The superconductivity is caused by the formation and condensation of pairs of electrons. Could there be condensates involving the formation of electron quadruplets? Such states are impossible within the paradigm of the standard Bardeen-Copper-Schrieffer theory. However, in the last two decades, different theoretical mechanisms were proposed, pointing to the tantalizing possibility that electron quadrupling condensates may exist. Severa years ago, an international experimental consortium collaborating with our theory group reported the first clear evidence of electron quadrupling condensate. This new state of matter was found in Ba1−xKxFe2As2 in the vicinity of x=0.8. In this project we will investigate the properties and understand the nature of this new state of matter. Besides that, in recent years, there were many other experimental breakthroughs in condensed-matter systems that exhibit multicomponent many-body degrees of freedom, making it a rich emergent field of research. As a consequence of having several types of carriers responsive for superconductivity, these materials behave fundamentally differently from traditional superconductors. These superconducting states require theoretical understanding from the fundamental viewpoint, and also in order to use such materials in practical applications, which we plan to address in the project. The proposal's third focus area is materials that can be used for quantum computers and quantum emulators.