Rock, Paper, Scissors 3-part
Naming
Java classes start with a capital letter and do not use underscores, so rock_paper should be RockPaper. Java uses camelCase, not snake_case, for all variable names except constants (static finals), so user_choice should be userChoice.
Spacing
The convention in java is to include whitespace before and after operators such as +, =, != or ==, so count_win=0 should be countWin = 0. Curly braces should be on the same line as an if or else.
Variable Declarations
You declare a new Random() inside your loop, so you might wind up making 19 Random objects, when you only need one. Declare it outside the loop. Conversely, you declare user_choice and computer_choice outside the loop, but they're only used inside. They should have the smallest possible scope.
Branching
You're branching (using if conditional statements) a lot to look up the name of a numeric selection. If you've learned about arrays, you could use a String[] of choices to simplify that lookup. There are a ton more branches to determine who wins. You only need one comparison to determine if there's a tie, and then only three specific checks to see if the user wins. Otherwise, the computer wins.
Making all those changes might look something like this:
import java.util.Random;
import java.util.Scanner;

public final class RockPaperScissors {

    private static final String[] CHOICES = { &quot;rock&quot;, &quot;paper&quot;, &quot;scissors&quot; };

    public static void main(final String[] argv) {
        final Random random = new Random();
        final Scanner keyboard = new Scanner(System.in);

        int computerWins = 0;
        int userWins = 0;

        System.out.println(&quot;\n Let us play Rock Paper Scissors \n&quot;);
        while (computerWins &lt;= 10 &amp;&amp; userWins &lt;= 10) {

            /* Read user input and determine choice */    
            System.out.println(&quot;\n Enter your choice 0 for rock, 1 for paper, or 2 for scissors \n&quot;);
            final int userChoice = keyboard.nextInt();
            if (userChoice &lt; 0 || userChoice &gt; 2) {
                System.out.println(&quot;Incorrect choice&quot;);
                continue;
            } else {
                System.out.println(&quot;\n Your choice was \n&quot; + CHOICES[userChoice]);
            }

            /* Randomly generate computer input */
            final int computerChoice = random.nextInt(3) + 1;
            System.out.println(&quot;\n The computer choice was \n&quot; + CHOICES[computerChoice]);

            if (userChoice == computerChoice) {
                System.out.println(&quot;Tie&quot;);
                continue;
            }

            if (userChoice == 0 &amp;&amp; computerChoice == 1
                    || userChoice == 1 &amp;&amp; computerChoice == 2
                    || userChoice == 2 &amp;&amp; computerChoice == 0) {
                System.out.println(&quot;\nThe user wins!&quot;);
                userWins++;
            } else {
                System.out.println(&quot;\nThe computer wins!&quot;);
                computerWins++;
            }
        }
    }
}

Review Note: I intentionally don't close the Scanner because I'm assuming that hasn't been covered yet.