Homebrew is a free and open-source package management system that simplifies the installation of software on macOS and Linux. It allows users to install, update, and manage software packages easily through the command line. Homebrew is known for its extensibility and has gained popularity for its ease of use and integration into the command-line interface.  # **Installation Paths for Homebrew Packages on macOS** The default installation paths for Homebrew packages on macOS vary depending on the system architecture: • **Apple Silicon (M1 and later):** Packages are installed in /opt/homebrew/.  • **Intel-based Macs:** Packages are installed in /usr/local/.  Within these directories, Homebrew organizes installed packages as follows: • **Cellar Directory:** Each package is installed in its own subdirectory within the Cellar directory. For example, if you install wget, it might reside in /opt/homebrew/Cellar/wget/ on Apple Silicon Macs.  • **Symlinks in bin:** To make executables easily accessible, Homebrew creates symbolic links (symlinks) in the bin directory. For instance, the wget executable would be symlinked to /opt/homebrew/bin/wget.  **Accessing Installed Packages via the Command Line** When you use the command line to execute programs, you’re typically running **binary executables**. These binaries are compiled machine code that the operating system can execute directly. In the context of Homebrew: • **Executable Binaries:** Homebrew installs the binary files of packages into its directory structure, making them executable from the command line. • **PATH Environment Variable:** To ensure that the shell can locate these executables, the directory containing the symlinks (e.g., /opt/homebrew/bin/ or /usr/local/bin/) must be included in your PATH environment variable. This inclusion allows you to run installed programs by simply typing their names in the terminal.  By managing the installation paths and updating the PATH variable accordingly, Homebrew ensures that installed software is readily accessible from the command line, streamlining the process of software management on macOS.