Can a normal Class implement multiple interfaces?

In a word - yes. Actually, many classes in the JDK implement multiple interfaces. E.g., ArrayList implements List, RandomAccess, Cloneable, and Serializable.

public class A implements C,D {...} valid

this is the way to implement multiple inheritence in java

Yes, a class can implement multiple interfaces. Each interface provides contract for some sort of behavior. I am attaching a detailed class diagram and shell interfaces and classes.

Ceremonial example:

public interface Mammal {
    void move();
    boolean possessIntelligence();
}

public interface Animal extends Mammal {
    void liveInJungle();
}

public interface Human extends Mammal, TwoLeggedMammal, Omnivore, Hunter {
    void liveInCivilization();
}

public interface Carnivore {
    void eatMeat();
}

public interface Herbivore {
    void eatPlant();
}

public interface Omnivore extends Carnivore, Herbivore {
    void eatBothMeatAndPlant();
}

public interface FourLeggedMammal {
    void moveWithFourLegs();
}

public interface TwoLeggedMammal {
    void moveWithTwoLegs();
}

public interface Hunter {
    void huntForFood();
}

public class Kangaroo implements Animal, Herbivore, TwoLeggedMammal {
    @Override
    public void liveInJungle() {
        System.out.println("I live in Outback country");
    }

    @Override
    public void move() {
        moveWithTwoLegs();
    }

    @Override
    public void moveWithTwoLegs() {
        System.out.println("I like to jump");
    }

    @Override
    public void eat() {
        eatPlant();
    }

    @Override
    public void eatPlant() {
        System.out.println("I like this grass");
    }

    @Override
    public boolean possessIntelligence() {
        return false;
    }
}

public class Lion implements Animal, FourLeggedMammal, Hunter, Carnivore {
    @Override
    public void liveInJungle() {
        System.out.println("I am king of the jungle!");

    }

    @Override
    public void move() {
        moveWithFourLegs();
    }

    @Override
    public void moveWithFourLegs() {
        System.out.println("I like to run sometimes.");
    }

    @Override
    public void eat() {
        eatMeat();
    }

    @Override
    public void eatMeat() {
        System.out.println("I like deer meat");
    }

    @Override
    public boolean possessIntelligence() {
        return false;
    }

    @Override
    public void huntForFood() {
        System.out.println("My females hunt often");
    }
}

public class Teacher implements Human {
    @Override
    public void liveInCivilization() {
        System.out.println("I live in an apartment");
    }

    @Override
    public void moveWithTwoLegs() {
        System.out.println("I wear shoes and walk with two legs one in front of the other");
    }

    @Override
    public void move() {
        moveWithTwoLegs();
    }

    @Override
    public boolean possessIntelligence() {
        return true;
    }

    @Override
    public void huntForFood() {
        System.out.println("My ancestors used to but now I mostly rely on cattle");
    }

    @Override
    public void eat() {
        eatBothMeatAndPlant();
    }

    @Override
    public void eatBothMeatAndPlant() {
        eatPlant();
        eatMeat();
    }

    @Override
    public void eatMeat() {
        System.out.println("I like this bacon");
    }

    @Override
    public void eatPlant() {
        System.out.println("I like this broccoli");
    }
}

A Java class can only extend one parent class. Multiple inheritance (extends) is not allowed. Interfaces are not classes, however, and a class can implement more than one interface.

The parent interfaces are declared in a comma-separated list, after the implements keyword.

In conclusion, yes, it is possible to do:

public class A implements C,D {...}