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Is their any class/classes inside java root package

The below code has no compilation error:-
import java.*;
class Test{
public static void main(String[] args){
}
}
My question is does the package named java only includes sub-packages or it also includes any class/classes. If yes then which class(s). If no then why we are able to import it.

There are no class directly under java. All the JDK's classes are under subpackages.
Having an empty package (or a package with no classeses in it) is perfectly legal in Java. You can import all the classes in it (which is no classes) with the * syntax. This isn't wrong - it's just pointless.

Where am I going wrong in trying to import a class?

Here's the code for the source file:
package moa4;
public class Book {
....
}
And for the destination file:
import moa4.Book;
public class Library {
...
}
The source and the destination are both saved in the same directory with the address:
C:\Users\\java\M\moa4
I'm getting the following error: package moa4 does not exist

You asked Library to import a package moa4.Book but you defined no such package. Instead, you defined a type Book inside package moa4, and that is not consistent with your import directive.
You could either import the package, or make that an import static of the class, but since Book and Library are both in the same package you don't need the import directive at all.
As mentioned, C:/Users/java/M needs to be in your classpath ("-cp" option).

eclipse: import (classname) cannot be resolved

I am new in using eclipse java using multiple .java files. My eclipse java project consist of one project file two package files, each with one .java class
My 2nd java class import the 1st java class/package, like so
VerifyLogin.java
package VerifyLogin;
import ArgumentCountException;
ArgumentCountException.java
// ...
The problem is VerifyLogin.java is getting an error
Import ArgumentCountException cannot be resolved
Or any reference I have to ArgumentCountException cannot be resolved to a type.

In java if you need to import a class then you need to use the full qualified name for that class, as the following:
import packageName.YourClass;
For Example, if your need to use Scanner class, then you need to import it as:
import java.util.Scanner;
But if the class was withing the same package, you don't need to import it.

When importing your class, it should be done as below:
//Current package name for the VerifyLogin Class (All package names should be lowercase by convention)
package packageforcurrentclass;
//Import statements: import thedependencyclasspackage.thedependencyclassname
import exceptionpackage.ArgumentCountException;
public class VerifyLogin
{
...
}

Getting Error for package name in netbeans

I am using one .java file and i have given a package name as com.onlinmebank but netbeans displaying error at this package declaration line as Incorrect Package.
Following is the package declaration code.
package com.onlinebank;
import java.sql.*;
import java.util.*;
public class BankCommons{
//All Code Here
}
Can Anybody tell me why i am getting this error

All Java keywords are lower-case!
So, this should work:
package com.onlinebank;
import java.sql.*;
import java.util.*;
public class BankCommons {
//All Code Here
}
And keep in mind, that the file BankCommons.java must be placed in the directory com/onlinebank.

In package, p should be small not Package(no captial P).
Also in public class p should be small. Similarily for Import also.
Important note all java keywords are in lower cases

Using classes in my project that originate in a jar file

I'm using Eclipse on a Windows 7 64x machine. I've researched this problem and found many have had a similar one, but no solution I came across quite worked for me.
I'm working on a Project named Assignment_1, on a class named Percolation. I'd like to use the object WeightedQuickUnionUF which is inside a package contained within a jar file, named algs4.jar.
I seem to have added the Jar file I'm interested in to the build-path (it now appears under "Referenced Libraries"). The jar file algs4.jar resides in a folder named lib inside my project's folder.
However, when I try to declare an object of type WeightedQuickUnionUF inside my class, I get an error "WeightedQuickUnionUF cannot be resolved to a type".
I tried various import commands (including just import WeightedQuickUnionUF )before the class declaration and all of them yield the error "The import so and so cannot be resolved".
For example, this piece of code yields both of these errors. One at the import line, and another at the declaration of the WeightedQuickUnionUF object:
package assignment_1_package;
import algs4.WeightedQuickUnionUF;
public class Percolation {
private int[][] grid;
public int gridDimension;
private int opensGrid[][];
private WeightedQuickUnionUF model;
... //rest of class body here
This has baffled me for an entire day and I can't seem to figure this out. Thanks for your efforts.
Edit: here is a link to the class I wish to import: http://algs4.cs.princeton.edu/15uf/WeightedQuickUnionUF.java.html

Assuming you are talking about the algs4.jar of the class http://algs4.cs.princeton.edu/code/ , your import is incorrect you should do :
import WeightedQuickUnionUF;
BUT it's never a good idea to have class in the default package and it's actually not allowed to import a type from the unnamed package: this gives a compilation error.
http://docs.oracle.com/javase/specs/jls/se5.0/html/packages.html#7.4.2:
A type-import-on-demand declaration (§7.5.2) imports all the
accessible (§6.6) types of a named type or package as needed. It is a
compile time error to import a type from the unnamed package.
So in your case to solve your issue just create your classes in the default package so you don't have to do the import at all.

I'm in the same class, had the same problem. Removing my equivalent to these two statements
package assignment_1_package;
import algs4.WeightedQuickUnionUF;
resolved the problem. That's to say the following now resolves correcly
private WeightedQuickUnionUF model;

In my case, it helped adding
import edu.princeton.cs.algs4.StdRandom;
import edu.princeton.cs.algs4.StdStats;
import edu.princeton.cs.algs4.WeightedQuickUnionUF;