What is the composition of the Universe in terms of Types Of Stars? There are 


Main Sequence Stars
Red Giants
White Dwarfs
Red Dwarfs
Neutron Stars
and other types of Stars.


How many % of stars are Main Sequence? How many are Red Giants? and so on.

I searched around and found some info, but it's confusing me. For example, 
I found that 90% stars are Main Sequence Stars, but at the same time, Red Dwarfs are the most common stars in the universe with 70%. What is true?
First of all, there is a misconception in your question that red dwarfs and main sequence stars are two completely different kinds of stars. 

Red dwarfs are a type of main sequence star. If a star is in the main sequence that just means that it is at a certain stage of its evolution. 
On the main sequence, stars can be further categorized based on their color into brown dwarfs, red dwarfs, sun-like stars, blue stars,...



In a comment, you state that the local distribution of stars is enough for your purpose.

To get the local distribution of star types, you can use the Gaia data, which gives the distance, luminosity and color of many stars in our galaxy. From this, you can plot an HR diagram, where the position of a star indicates its type..



This diagram isn't quite correct, because it uses a cut in magnitude to select stars. This means that fainter stars are under-sampled. But if you only took stars up to a certain distance, you could get something more representative. 

In this article, you have a breakdown of stars based on their intrinsic luminosity and their spectral class. Most stars (76%) are in the main sequence, 24% are white dwarfs, and the rest (0.6%) are on the giant branch.



The stellar distribution of our Milky Way seems to be pretty typical for this type of galaxy, but there are other types of galaxies where the stellar distribution is rather different. When a galaxy is rather young, there is a lot of gas available for new stars to form, so you get a lot of big bright blue stars. But these big stars are short-lived, so in elliptical galaxies where the stellar population is older, you get more small red stars. 

Finding the distribution of star types in these different types of galaxies is the matter of stellar population synthesis. You start out with an initial mass function (IMF) that tells you the number of stars there are with any given mass in one galaxy. This gives you a snapshot of the galaxy at time t=0. Then you use stellar evolution models to see how that initial population evolves over time. 

De Marchi et al gives the IMF for a cluster of galaxies (rather than for individual galaxies). This might be as close to a "typical" distribution as you can get. 



Further reading