Welcome aboard our exploration of the building block of Neural Networks: the perceptron! This significant algorithm sparks your comprehension of advanced Neural Networks utilized in Machine Learning. The objectives of this lesson include mastering and coding a perceptron using Python from scratch. We will decipher the structure of a perceptron, the prediction method, and the training process. To conclude, we will design a fully functioning model that abstracts a simple logical scenario using the AND operator data.

We start by delving into the perceptron, a simple form of binary linear classifiers in the Neural Network family. A perceptron operates by accepting multiple inputs, aggregating them, and democratically deciding the output based on these inputs.

Think of perceptrons as a democratic process. Each "voter" (input) contributes with differing weights. The "candidate" (output) who secures the majority of votes (aggregate of weighted inputs) wins and is chosen.

Mathematically, the predicted output of a perceptron can be formulated as follows: