Update documentation sections (#5452)

Reframes "the low-level interface" as "the pip interface"
Adds indexes to all sections
Renames "commercial indexes" to "alternative indexes"

docs/concepts/python-versions.md

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+# Python versions
+
+A Python version is composed of a Python interpreter (i.e. the `python` executable), the standard library, and other supporting files. It is common for an operating system to come with a Python version installed.
+
+## Requesting a version
+
+uv will automatically download a Python version if it cannot be found.
+
+For example, when creating a virtual environment:
+
+```bash
+uv venv --python 3.11.6
+```
+
+uv will ensure that Python 3.11.6 is available — downloading and installing it if necessary — then create the virtual environment with it.
+
+Many Python version request formats are supported:
+
+- `<version>` e.g. `3`, `3.12`, `3.12.3`
+- `<version-specifier>` e.g. `>=3.12,<3.13`
+- `<implementation>` e.g. `cpython` or `cp`
+- `<implementation>@<version>` e.g. `cpython@3.12`
+- `<implementation><version>` e.g. `cpython3.12` or `cp312`
+- `<implementation><version-specifier>` e.g. `cpython>=3.12,<3.13`
+- `<implementation>-<version>-<os>-<arch>-<libc>` e.g. `cpython-3.12.3-macos-aarch64-none`
+
+## Installing a Python version
+
+Sometimes it is preferable to install the Python versions before they are needed.
+
+uv bundles a list of downloadable CPython and PyPy distributions for macOS, Linux, and Windows.
+
+To install a Python version at a specific version:
+
+```bash
+uv python install 3.12.3
+```
+
+To install the latest patch version:
+
+```bash
+uv python install 3.12
+```
+
+To install a version that satisfies constraints:
+
+```bash
+uv python install '>=3.8,<3.10'
+```
+
+To install multiple versions:
+
+```bash
+uv python install 3.9 3.10 3.11
+```
+
+## Project Python versions
+
+By default `uv python install` will verify that a managed Python version is installed or install the latest version.
+
+However, a project may define a `.python-version` file specifying the default Python version to be used. If present,
+uv will install the Python version listed in the file.
+
+Alternatively, a project that requires multiple Python versions may also define a `.python-versions` file. If present,
+uv will install all of the Python versions listed in the file. This file takes precedence over the `.python-version` file.
+
+uv will also respect Python requirements defined in a `pyproject.toml` file during project command invocations.
+
+## Viewing available Python versions
+
+To list installed and available Python versions:
+
+```bash
+uv python list
+```
+
+By default, downloads for other platforms and old patch versions are hidden.
+
+To view all versions:
+
+```bash
+uv python list --all-versions
+```
+
+To view Python versions for other platforms:
+
+```bash
+uv python list --all-platforms
+```
+
+To exclude downloads and only show installed Python versions:
+
+```bash
+uv python list --only-installed
+```
+
+## Adjusting Python version preferences
+
+By default, uv will attempt to use Python versions found on the system and only download managed interpreters when necessary.
+However, It's possible to adjust uv's Python version selection preference with the `python-preference` option.
+
+- `only-managed`: Only use managed Python installations; never use system Python installations
+- `installed`:    Prefer installed Python installations, only download managed Python installations if no system Python installation is found
+- `managed`:      Prefer managed Python installations over system Python installations, even if fetching is required
+- `system`:       Prefer system Python installations over managed Python installations
+- `only-system`:  Only use system Python installations; never use managed Python installations
+
+These options allow disabling uv's managed Python versions entirely or always using them and ignoring any existing system installations.
+
+## Discovery order
+
+When searching for a Python version, the following locations are checked:
+
+- Managed Python versions in the `UV_PYTHON_INSTALL_DIR`.
+- A Python interpreter on the `PATH` as `python3` on macOS and Linux, or `python.exe` on Windows.
+- On Windows, the Python interpreter returned by `py --list-paths` that matches the requested
+  version.
+
+If a specific Python version is requested, e.g. `--python 3.7`, additional executable names are included in the search:
+
+- A Python interpreter on the `PATH` as, e.g., `python3.7` on macOS and Linux.
+
+## Python distributions
+
+Python does not publish official distributable CPython binaries, uv uses third-party standalone distributions from the [`python-build-standalone`](https://github.com/indygreg/python-build-standalone) project. The project is partially maintained by the uv maintainers and is used by many other Python projects.
+
+The Python distributions are self-contained and highly-portable. Additionally, these distributions have various build-time optimizations enabled to ensure they are performant.
+
+These distributions have some behavior quirks, generally as a consequence of portability. See the [`python-build-standalone` quirks](https://gregoryszorc.com/docs/python-build-standalone/main/quirks.html) documentation for details. 
+
+PyPy distributions are provided by the PyPy project.