Technical summary
The ESP-01 module is a small module built around an ESP8266, and it is the smallest of these modules. It lets you connect any microcontroller (as long as it has a UART Rx/Tx) to a WiFi network. The module has 8 pins and must be powered with 3.3V. But be careful, there are two kinds: a blue one with 512MB of memory and a black one (as shown below) with 1024MB. For this example, we will use the 1024 version, also called ESP-01S.
