# Using StandardScaler function of scikit-learn library

I have been using the StandardScaler function from the sklearn library. Could you tell me how it normalizes the distribution in order to convert it into a Gaussian distribution?

The StandardScaler function from the sklearn library actually does not convert a distribution into a Gaussian or Normal distribution. It is used when there are large variations among the distribution values. It simply is a Feature Scaling method used to standardize the distribution making the values lie in the same range.
Not limited to scikit-learn, standardization does not convert features/variables into a normal distribution. It just subtracts the mean and divides by the standard deviation. The resulting feature will have a mean $$0$$ and a variance $$1$$. This has nothing to do with normal distribution.
In essence, the following affine transform doesn't convert random variables into normal RV: $$Z=\frac{X-\mu}{\sigma}$$