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Can't load main class

It's a simple class and I am a beginner with Java.
I don't know why this code is not running and why it gives an error :
Could not find or load main class
class tuto{
public static void main(String[] args){
System.out.println("Hello World");
}
}

There are a couple things which jump out at me when I look at your question.
The first thing is that you have unresolved compiler errors. If you see that red 'x' on the Problems tab, you should fix all the errors there before trying to run anything.
The second thing is that your class name doesn't match the file name in which it is defined. For public classes the name of the class and the name of the file must match, and while your class isn't public, this is a widely followed Java convention and you will confuse people if you don't follow it.
As to your actual question, my best guess is that you have placed your class into a package and not declared it as such in your source code. If you go look at the Problems tab, it will tell you what is wrong and (often) how to fix it.
I can approximate your error message if I do the following:
In this case, I have an error over in the Problems tab complaining about the declared package.
Check to see if you have something similar:
If you do, you can right-click the error message and select "Quick Fix", and eclipse will pop up a dialog offering to add the package declaration for you:

In your code there is a compile error, that is because Syteme change it to System
Syteme.out.println("Hello World");
should be
System.out.println("Hello World");
P.S
And in Java when you have a public class in a file, then file name must be that class name. It is a must. Otherwise you will get an error.
If you have this class in a package then you must specify the package declaration first
e.g
package abc;

System.out.println not Syteme.out.println.
In Java (as somebody has already pointed) the name of the file should be of the same name of the main class within the same file.
Moreover, you should also declare an array using this syntax array_type [] array_id and not array_type array_id [].

There might be a couple of problems:
If the class is in a package, make sure you specify it. eg: package com.pak;
The class with main method always needs to be public. public class apples{}

How to mention the class path

How can I mention the path of a class as in following code?
Class cl=Class.forName("SomeClass");
This works well if the "SomeClass" is located in the same directory of the calling class. But how to check for a class from a different directory, I saw the syntax for that is like xxxx.yyyy.class, but could not make out what those 'x's and'y's stand for. please help.
Thanks in advance.

Use the fully-qualified class name. For instance, to do this with the Java SE String class, which is in the java.lang package:
Class clazz = Class.forName("java.lang.String");

Those xxx and yyy stands for package names. Packages are normally represented by directories on disk with the same name as the package. When you create a class file you can specify which package the class goes by stating package xxx.yyy at the top of the file.
Referring to "SomeClass" without a package name will try to load a class named SomeClass in the default package.

Use Class.forName although make sure you deal with a possible ClassNotFoundException exception. This is a runtime exception so it does not mean you need to catch it. This is how you will know if you path to the class is correct. The problem is that if it cannot find the class funny things can happen with your code.
Class.forName(com.my.package.ClassName)

Why don't I have to import a class I just made to use it in my main class? (Java)

I am currently learning Java using the Deitel's book Java How to Program 8th edition (early objects version).
I am on the chapter on creating classes and methods.
However, I got really confused by the example provided there because it consists of two separate .java files and when one of them uses a method from the other one, it did not import the class. It just created an object of that class from the other .java file without importing it first.
How does that work? Why don't I need to import it?
Here is the code from the book (I removed most comments, to save typing space/time...):
.java class:
//GradeBook.java
public class GradeBook
{
public void displayMessage()
{
System.out.printf( "Welcome to the grade book!" );
}
}
The main .java file:
//GradeBookTest.java
public class GradeBookTest
{
public static void main( String[] args)
{
GradeBook myGradeBook = new GradeBook();
myGradeBook.displayMessage();
}
}
I thought I had to write
import GradeBook.java;
or something like that.
How does the compiler know where GradeBook class and its methods are found and how does it know if it exists at all if we dont import that class?
I did lots of Googling but found no answer.
I am new to programming so please tolerate my newbie question.
Thank you in advance.

It is because both are in same package(folder). They are automatically imported no need to write import statement for that.

You don't have to import classes that are in the same package as the current class.
Also, note that GradeBook.java is the name of the file. The (simple) name of the class is GradeBook. Every class should be in a package. If it is in the package com.foo.bar, the class name is com.foo.bar.GradeBook, and this is the name you must use when importing this class.
Read http://download.oracle.com/javase/tutorial/java/package/packages.html to learn more about packages.

The classes located in the same package do not have to be imported, as they are visible to each other. You simply import a class that is in another package:
import java.util.ArrayList;
Note that you are not importing the file, but the class.

It's all about packages. You are trying to use a class from the default package which does not need explicit import of the java file, ie GradeBook inside GradeBookTest
Here is where you can start with learning about packages :
Java Package Tutorial
and :
Creating and Using Packages

Java doesn't use includes the way C does. Instead java uses a concept called the classpath, a list of resources containing java classes. The JVM can access any class on the classpath by name so if you can extend classes and refer to types simply by declaring them.
From: Include one java file in another java file

Imports are for importing classes that are in a different package. Since you didn't declare a package for either they are both put in the default package. The compiler can find it because the class lives in the same directory.

You don't have to import classes which are in the same package.

Well, classes in the same package are automatically imported.

They're in the same package. This tutorial will do more justice than I will.

What should be the name of a Java source that contains more than one class?

If there is more than one class in one Java source file then what will be the file name of the .java file?

there can only be one public top level class in a java file. The name of the public class must match that of the file name. Other than this, there can be as many non public (default/package access) classes as you like.
None of this is part of any java specification, it is just convention but a very convenient one. This 'convention' also includes such things as java and class files being found in directory structures matching the package name of the class. Check out the java tutorial on this.

Only one class can be public in the same file and the public class is the file name...

Defining classes in Java files

I have found one error in my Java program:
The public type abc class must be defined in its own class
How can I resolve this error? I am using Eclipse. I am new to Java programming.

Each source file must contain only one public class. A class named ClassName should be in a file named ClassName.java, and only that class should be defined there.
Exceptions to this are anonymous and inner classes, but understanding you are a beginner to Java, that is an advanced topic. For now, keep one class per file.
Answering your addition: it is OK to inherit classes and that's totally fine. This does not matter, each class should still have its own file.

Public top-level classes (i.e. public classes which aren't nested within other classes) have to be defined in a file which matches the classname. So the code for class "Foo" must live in "Foo.java".
From the language specification, section 7.6:
When packages are stored in a file system (§7.2.1), the host system may choose to enforce the restriction that it is a compile-time error if a type is not found in a file under a name composed of the type name plus an extension (such as .java or .jav) if either of the following is true:
The type is referred to by code in other compilation units of the package in which the type is declared.
The type is declared public (and therefore is potentially accessible from code in other packages).
This rule, which doesn't have to be followed by compilers, is pretty much universally adhered to.

Ok, maybe an example will help.
In file MySuperClass.java:
public class MySuperClass {
// whatever goes here
}
public class MySubClass1 extends MySuperClass {
// compile error: public class MySubClass1 should be in MySubClass1.java
}
class MySubClass2 extends MySuperClass {
// no problem (non-public class does not have to be in a file of the same name)
}
In file MySubClass3.java:
public class MySubClass3 extends MySuperClass {
// no problem (public class in file of the same name)
}
Does that make things clearer?

A public class with the name of "abc" must be in a file called abc.java

You can create a new class an a existing file if it's private, but you should not do this.
Create one file per class.
Eclipse does that for you, if you create a new class.
For programming Java, you have to understand the construct of classes, packages and files. Even if Eclipse helps you, you have to know it for yourself. So start reading Java books or tutorials!