Greetings Machine Learning enthusiast! Let's take a deep dive into the fascinating realm of neural networks. Specifically, we'll focus on constructing a neural network using the Pythonic TensorFlow library.

Neural networks attract global interest due to their capabilities of learning patterns from vast volumes of complex data, thus mimicking the learning ethos of the human brain. They have broken the barriers of conventional computing and have ushered in a new era where machines can understand complex tasks that were once exclusive to human intellect.

In today's tutorial, we'll explore how to build these intelligent systems by leveraging TensorFlow's robust functionalities. Our goal is to give you a behind-the-scenes look at the inner workings of these systems.

TensorFlow, an open-source library developed by the Google Brain Team, serves as a powerful tool for numerical computations, making it a popular choice for large-scale machine learning.

Let's familiarize ourselves with the triarchy of TensorFlow's architecture:

1. Tensors: These are essentially multi-dimensional arrays with a standardized type and act as the heart of TensorFlow.

2. Computation Graphs: TensorFlow operates using 'lazy execution.' It first designs a computational graph representing various tensor operations, which are then executed in sessions.

3. Sessions: Within the realm of TensorFlow, computations don't manifest instantaneously. They run within a scope called a session.

TensorFlow provides numerous utilities and methods to design, train, and execute neural networks, making it a powerful asset in any neural network project. It manages the low-level nuances, allowing you to concentrate more on improving your model.

Before we dive into creating a neural network, let's understand its structure. Neural networks consist of a compilation of interconnected artificial neurons or "nodes." They typically comprise three types of layers:

1. Input layer: This is the starting point for the data's journey within the network (labeled in the above image as I1, I2, I3).
2. Hidden layers: These layers handle the heavy lifting. They perform computations and extract useful features from the data (the unlabeled layers in the above image).
3. Output layer: This is the layer that provides the final result (labeled in the above image as O1, O2).

Each layer plays a significant role, similar to neurons in our brain. When neurons in our brains receive inputs, they process them and generate outputs. This exact mechanism occurs in a neural network. The number of input nodes in the input layer depends on the type of data we are working with and the number of output nodes in the output layer depends on the type of prediction we are making.

As far as the number of hidden layers and shape, that's where the art of Machine Learning comes in. There is no one best way to construct a neural network though there are best practices. It comes down to getting a deep understanding of the dataset and continuously experimenting.

Next, we have "activation functions" — one of the most critical aspects of neural networks. An activation function decides whether a neuron contributes to the next layer based on its input.

In the next section you'll see an example where, relu and softmax are activation functions. relu allows positive values to pass while replacing negative values with zeros. On the other hand, softmax transforms a list of numbers into a probability distribution.

Next time we'll go a little deeper into the mathematical representation of neural networks but for now let's see how to create them in TensorFlow.