Logistic Regression Explained from Scratch (Visually, Mathematically and Programmatically)

A plethora of results appear on a small google search "Logistic Regression". Sometimes it gets very confusing for beginners in data science, to get around the main idea behind logistic regression. And why wouldn't they be confused!!? Every different tutorial, article, or forum has a different narration on Logistic Regression (not including the legit verbose of textbooks because that would kill the entire purpose of these "quick sources" of mastery). Some sources claim it a "Classification algorithm" and some more sophisticated ones call it a "Regressor", however, the idea and utility remain unrevealed. Remember that Logistic regression is the basic building block of artificial neural networks and no/fallacious understanding of it could make it really difficult to understand the advanced formalisms of data science.