update README

README.md

@@ -5,7 +5,7 @@
 
 # BlockTensorKit
 
-Contains code for handling `BlockTensorMaps`, which are the [TensorKit.jl](https://github.com/jutho/TensorKit.jl) equivalent of BlockArrays.
+*A Julia package for handling arrays-of-tensors, built on top of [TensorKit.jl](https://github.com/Jutho/TensorKit.jl)*
 
 | **Documentation** | **Build Status** | **Coverage** | **Quality assurance** |
 |:-----------------:|:----------------:|:------------:|:---------------------:|
@@ -16,7 +16,7 @@ Contains code for handling `BlockTensorMaps`, which are the [TensorKit.jl](https
 [docs-stable-url]: https://lkdvos.github.io/BlockTensorKit.jl/stable
 
 [docs-dev-img]: https://img.shields.io/badge/docs-dev-blue.svg
-[docs-dev-url]: https://lkdvos.github.io/BlockTensorKit.jl/latest
+[docs-dev-url]: https://lkdvos.github.io/BlockTensorKit.jl/dev
 
 [ci-img]: https://github.com/lkdvos/BlockTensorKit.jl/actions/workflows/CI.yml/badge.svg
 [ci-url]: https://github.com/lkdvos/BlockTensorKit.jl/actions/workflows/CI.yml
@@ -28,4 +28,16 @@ Contains code for handling `BlockTensorMaps`, which are the [TensorKit.jl](https
 [aqua-url]: https://github.com/JuliaTesting/Aqua.jl
 
 
+In the context of developing efficient tensor network algorithms, it can sometimes be convenient to write a tensor as a concatenation of other tensors, without explicitly merging them.
+This is helpful whenever there are some guarantees on the resulting structure, such as sparsity patterns, triangular structures, or just as a way of keeping things organized.
+One particular example, for which this package is primarily developed, is the construction of Matrix Product Operators (MPOs) that represent a sum of local operators, both on 1-dimensional geometries, but also for more general tree-like geometries.
+In those cases, the combination of an upper-triangular blocked structure, as well as efficient usage of the sparsity, can not only greatly speed up runtime, but also facilitates rapid development of novel algorithms.
 
+Mathematically speaking, we can consider these blocked tensors as acting on direct sums of vector spaces, where the indiviual vector spaces are supplied by TensorKit.
+This leads to a very natural generalization of `AbstractTensorMap`, which is able to handle arbitrary symmetries.
+
+BlockTensorKit.jl aims to provide a convenient interface to such blocked tensors.
+In particular, the central types of this package (`<:AbstractBlockTensorMap`) could be describes as having both `AbstractArray`-like interfaces, which allow indexing as well as slicing operations, and `AbstractTensorMap`-like interfaces, allowing linear algebra routines, tensor contraction and tensor factorization.
+The goal is to abstract away the need to deal with the inner structures of such tensors as much as possible, and have the ability to replace `AbstractTensorMap`s with `AbstractBlockTensorMap` without having to change the high-level code.
+
+For examples and further information, please check out the [documentation](https://lkdvos.github.io/BlockTensorKit.jl/dev).