Java provides several methods in the Character class for working with Unicode characters. Some of the commonly used methods are:

1. isDigit(char ch) - Returns true if the specified character is a digit, false otherwise.
2. isLetter(char ch) - Returns true if the specified character is a letter, false otherwise.
3. isWhitespace(char ch) - Returns true if the specified character is a whitespace character, false otherwise.
4. isUpperCase(char ch) - Returns true if the specified character is an uppercase letter, false otherwise.
5. isLowerCase(char ch) - Returns true if the specified character is a lowercase letter, false otherwise.
6. isTitleCase(char ch) - Returns true if the specified character is a titlecase letter, false otherwise.
7. toUpperCase(char ch) - Returns the uppercase equivalent of the specified character, if any.
8. toLowerCase(char ch) - Returns the lowercase equivalent of the specified character, if any.

Here's an example that demonstrates the use of some of these methods:

char ch = 'A';
if (Character.isUpperCase(ch)) {
    System.out.println(ch + " is an uppercase letter.");
}

if (Character.isLetter(ch)) {
    System.out.println(ch + " is a letter.");
}

char lowercaseCh = Character.toLowerCase(ch);
System.out.println(ch + " in lowercase is " + lowercaseCh);

This code checks if the character 'A' is an uppercase letter and a letter, and then converts it to lowercase using the toLowerCase() method and prints the result.

The Character class also provides methods for working with Unicode code points, including the codePointAt(), codePointBefore(), and codePointCount() methods. These methods allow you to manipulate and access individual code points in a string, which is important for correctly handling text in different languages and scripts.

In summary, the Character class in Java provides several methods for working with Unicode characters, including methods for checking the type of a character, converting characters to uppercase or lowercase, and manipulating code points in a string. By using these methods, developers can create software applications that correctly handle text in different languages and scripts.