In Elixir, immutable data structures are data structures whose values cannot be changed after they are created. Once a data structure is assigned a value, that value remains fixed and cannot be modified in-place.

Elixir embraces immutability as a core principle, meaning that variables and data structures are treated as immutable by default. Instead of modifying existing data, Elixir encourages creating new data structures based on existing ones, incorporating the desired changes.

Here are some commonly used immutable data structures in Elixir:

* Lists : Lists are ordered collections of elements. In Elixir, lists are implemented as linked lists, where each element points to the next element. Lists are immutable, so operations that appear to modify a list, such as appending an element, actually create a new list that includes the desired changes.

* Tuples : Tuples are ordered collections of elements. Unlike lists, tuples have a fixed length and can contain elements of different types. Tuples are also immutable, and creating a new tuple with modified or additional elements involves creating a completely new tuple.

* Maps : Maps are key-value data structures where each key is associated with a value. Maps in Elixir are implemented as hash arrays and provide efficient lookup and update operations. Like other immutable data structures, modifying a map involves creating a new map with the desired changes.
* Structs : Structs are user-defined data structures that provide a named field for each value. Structs are defined using the `defstruct` construct and are similar to maps, but with a defined structure. Structs in Elixir are also immutable, and modifying a struct involves creating a new struct with the desired changes.

* Binaries : Binaries are sequences of raw bytes. They are often used for handling binary data, such as network packets or file contents. Binaries in Elixir are immutable, and operations that appear to modify a binary, such as concatenation or slicing, create a new binary with the desired changes.


The immutability of these data structures ensures that once created, their values remain unchanged, providing several benefits, including:

* Simplified concurrency : Immutable data structures can be safely shared among concurrent processes without the need for locks or synchronization.
* Predictable and reliable code : Since data cannot be modified in-place, bugs related to unintended mutations are minimized, making code easier to reason about and debug.
* Efficient memory management : Immutable data structures allow for memory optimizations, such as structural sharing, where common parts of data structures can be shared, reducing memory usage.

By leveraging immutable data structures, Elixir promotes functional programming practices and enables the creation of reliable, scalable, and concurrent applications.