Mathematical logic concerns how one determines the truth or falsity of a statement(s). In existing logics (can be read as "systems of logic,") this involves large sets of notation and a significant amount of rewriting in proofs, which can and does get quite annoying quite quickly.
Logician Charles Peirce constructed the Existential Graph System to visualize several logics. For right now, we will discuss his Alpha Existential Graph System, which we will abbreviate as AEG System in reference to the system and AEGs in reference to Alpha Existential Graphs themselves, and we will assume you have no experience working in or understanding of other logics.
If the object seems intimidating, please continue still. One is able to conclude logical truths as a consequence of drawing ellipses and letters, which, while it sounds silly, is both true and good fun. If it is any motivation, all the same conclusions reachable in other, similar logics, which concern strictly truth and falsity, are reachable through the AEG System, even though it may seem somewhat counterintuitive at first glance that a visualization can be just as powerful.
To reiterate, before going into Chapter 1.1, it is very important to understand the first paragraph here. There are few numbers in these parts. While it is easy to get lost in seas of odd notation, it is helpful to remind oneself that the AEG System and systems similar were developed to discuss and verify, strictly, the truth or falsity of some statement and its components.