I am working on a biological dataset which is not following ideal normal/gaussian distribution.. Which statistical test and technique would be best to analyze this dataset ??
There are a variety of non-parametric methods to choose from, depending on the research question. It's difficult to give a general answer.
If it is testing differences between independent groups you are intereted in you can use Mann-Whitney's U-test, or Kolmogorov-Smirnov's test. For dependent data there are other tests.
If you provide more information I will be able to give you more detailed suggestions.
That information does not make your question clearer. You can substitute "difference" by "concentration difference" in my previous post and the questions remain the same.
If you want a statistical analysis then you must ask a statistical question.