Rumi says that death is of the body, not the soul. He says we are the soul, which can never die. On the death of the body, the soul will be free to meet its source, it's  lover - God. Re-birth depends on how we have led this life. If we lead an egoless life we will be able to be one with the Source. 

From Rumi's big treasure of poems, these were just a few, which I have attempted to translate in Hindi. 

Rumi says that women are not an object of lust. She is a Creator. He says the Almighty is a woman. The Creator has compassionate qualities, she is loving, caring, forgiving, empathetic, etc, which are all qualities inherent in women. Her love is for everybody and there is no need to fear Her. 

Rumi say that there is only One Existence. There is no individuality because we are part of the Almighty. We come from that One source and we will go back into that same source. We are never alone, as the Existence  is always with us. 
This word "Adwait" that is Oneness is the main concept of Indian philosophy too. 

Rumi says God is in every breath. She is love. Love is God and God is love. There is no form, no gender, no shape, no duality. It is pure love and love only. 

Rumi says if you are fully dedicated to God only then you can meet  and experience God. It's like a drop of water meeting the sea, it no longer remains a drop, but becomes the sea itself. Similarly, we can become a part of God, when we forget ourselves and dissolve ourselves in the ocean of God.

Rumi says through his poetry  that we need to accept whatever God has given us. So, if there is sadness, or pain, or happiness, or sickness, etc. we need to accept it completely. Don't bring your mind into the situation. Accept it as the will of God, without complaining. It is then, that the true meaning  of acceptance is understood.  

Rumi explains what is Love? He says that attraction  towards things, valuables, luxury items, or physical bodies is not love; it is lust, desire, greed. Love is something  beyond the body and mind. It is platonic. Is it attraction  of the hearts? We cannot say, but you become another person. When love comes in your heart, you will see happiness  everywhere and you will become a positive  person. 

Rumi through his poetry beautifully  explains that Love is the only medicine for all diseases. 

Rumi says that the first step is to realise that you are not getting peace and happiness from world things. It is then that you will look within and seek your inner self. It is in silence that we can hear our inner voice and our heart. To achieve silence we need to leave unnecessary thinking, talking and doing and become mind less/ empty the mind. 

Rumi says that one should not be mind full, and should not make the mind your Master. One should remember that you are the Master of your mind. The mind will keep you occupied in worldly things, and will not let you listen to your heart and your inner voice. Therefore, in order to be able to listen to your inner voice you need to remain silent and keep your mind empty.