According to Effective Java, chapter 4, page 73, 2nd edition:
"There are many good reasons for this: Immutable classes are easier to design, implement, and use than mutable classes. They are less prone to error and are more secure.
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"Immutable objects are simple. An immutable object can be in exactly one state, the state in which it was created. If you make sure that all constructors establish class invariants, then it is guaranteed that these invariants will remain true for all time, with no effort on your part.
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Immutable objects are inherently thread-safe; they require no synchronization. They cannot be corrupted by multiple threads accessing them concurrently. This is far and away the easiest approach to achieving thread safety. In fact, no thread can ever observe any effect of another thread on an immutable object. Therefore, immutable objects can be shared freely
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Other small points from the same chapter:
Not only can you share immutable objects, but you can share their internals.
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Immutable objects make great building blocks for other objects, whether mutable or immutable.
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The only real disadvantage of immutable classes is that they require a separate object for each distinct value.