Links to other tensor network resources:
Nishino's unofficial DMRG + tensor networks homepage
Frequently updated catalog of arXiv preprints pertaining to DMRG and tensor networks, maintained by Tomotoshi Nishino. Very useful to stay up to date with the latest research developments in tensor networks!
Introductory Tensor Network References
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"Handwaving and Interpretive Dance: An Introductory Course on Tensor Networks", by Jacob Bridgeman and Christoper Chubb

Well written and comprehensive introduction to the field of tensor networks, which also contains practice problems with worked solutions
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"A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States", by Roman Orus

Very gentle and pedagogical introduction to entanglement and tensor network states, focusing on MPS and PEPS
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"Tensor Network States and Geometry", by Glen Evenbly and Guifre Vidal

Slightly more advanced reference, focusing on the understanding of entanglement and correlations in tensor network states
"Renormalization and tensor product states in spin chains and lattices", by Ignacio Cirac and Frank Verstaete

Introduction to tensor networks states and methods from the perspective of the realspace renormalization group
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"Era of Big Data Processing: A New Approach via Tensor Networks and Tensor Decompositions", by Andrzej Cichocki

Introduction to tensor networks with a focus on their application to big data processing
Numerical Tensor Network Packages
iTensor
Library developed by Steve White and Miles Stoudenmire, written in C++ and focused on enabling highend DMRG and MPS based calculations
Universal Tensor Network Library  Uni10
Library designed for the development of tensor network algorithms, written in C++ but also providing Python wrappers
Tensor Operations
Easy to use Julia package for tensor contractions and related operations, developed by Jutho Haegeman
Tensor Network Python (TeNPy)
Python library for the simulation of strongly correlated quantum systems with tensor networks
Tensor Network Theory (TNT)
Library written in C aimed at providing a platform for rapidly developing robust, easy to use and highly optimized code for tensor network calculations.
Some Introductory Lectures
"Classical Simulation of Quantum Manybody Systems with Tensor Networks"
Glen Evenbly, Challenges in Quantum Computation Workshop,
(Simons Institute, Berkeley, June 2018)
"From qubits to entanglement, and then to Matrix Product States"
Roman Orus, Tensor Networks and Quantum Manybody Problems,
(ISSP, Tokyo University, June 2016)
"Introduction to the MERA"
Glen Evenbly, Tensor Networks and Quantum Manybody Problems,
(ISSP, Tokyo University, July 2016)