What is the prerequisiste to study Tensors for application in signal processing? I want to study Blind Source separation in signal processing for this I need to study Tensors and have a basic idea about rank, border rank and other concepts. Right now I am studying from Tensors:Geometry and Applications by J M Landsberg, but the language suggest that much more than linear algebra is needed to understand it.I know Basic linear algebra, but the notations and other complexity issues, along with spaces, proves to be a problem. Can anyone suggest me a way to understand Tensors or this book?

If you will browse papers on BSS, then you can notice that the authors make use of (numerical) linear algebra only.

I think the best (shortest) way to learn rank, border rank, canonical polyadic decomposition, higher-order singular values decomposition, tensor trains, etc. will be to read the following review papers:

1 T.G. Kolda; Brett W. Bader. Tensor Decompositions and Applications SIAM Review 2009 51:3, 455-500.

2 Cichocki, A.; Mandic, D.; De Lathauwer, L.; Guoxu Zhou; Qibin Zhao; Caiafa, C.; Phan, H.A. "Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis," Signal Processing Magazine, IEEE , vol.32, no.2, pp.145,163, March 2015.

The papers do not contain any proofs, but refer to original papers.

You can of course find related material on tensors in the Handbook of Blind Source Separation link