This paper presents a method for concentrating entanglement in quantum systems. The goal is to transform multiple partly-entangled pairs of particles into fewer maximally entangled pairs, such as singlets, using local operations and classical communication. The process, called entanglement concentration, asymptotically conserves the entropy of entanglement, with the yield of singlets approaching the base-2 entropy of entanglement of the initial partly-entangled pure state. Conversely, any pure or mixed entangled state can be produced by two separated observers using a supply of singlets as their sole source of entanglement. The paper discusses two methods for entanglement concentration: the Schmidt projection method and the Procrustean method. The Schmidt projection method involves projecting the joint state of n pairs of particles onto a subspace spanned by states with a common Schmidt coefficient. This method is efficient for large n, with the yield of singlets approaching nE - O(log n), where E is the entropy of entanglement of the initial state. The Procrustean method, which works even with a single partly entangled pair, involves discarding the extra probability of the larger term in the entangled state, leaving a perfectly entangled state. The paper also discusses the efficiency of entanglement concentration and its relation to quantum data compression. While quantum data compression can be used to approximate entanglement concentration, it is not as effective as the Schmidt projection method. The paper shows that two-sided quantum data compression does not work as a method of entanglement concentration, as it fails to produce maximally entangled states. Conversely, entanglement concentration by the Schmidt projection method necessarily sacrifices fidelity to the original state in order to produce a maximally entangled output. The paper concludes that entanglement concentration is a crucial process in quantum information theory, allowing the transformation of partly-entangled states into maximally entangled states. The Schmidt projection method is the most efficient method for this task, with the yield of singlets approaching the entropy of entanglement of the initial state. The paper also discusses the limitations of entanglement measures for mixed states and presents examples of entangled mixed states, such as the Werner state.This paper presents a method for concentrating entanglement in quantum systems. The goal is to transform multiple partly-entangled pairs of particles into fewer maximally entangled pairs, such as singlets, using local operations and classical communication. The process, called entanglement concentration, asymptotically conserves the entropy of entanglement, with the yield of singlets approaching the base-2 entropy of entanglement of the initial partly-entangled pure state. Conversely, any pure or mixed entangled state can be produced by two separated observers using a supply of singlets as their sole source of entanglement. The paper discusses two methods for entanglement concentration: the Schmidt projection method and the Procrustean method. The Schmidt projection method involves projecting the joint state of n pairs of particles onto a subspace spanned by states with a common Schmidt coefficient. This method is efficient for large n, with the yield of singlets approaching nE - O(log n), where E is the entropy of entanglement of the initial state. The Procrustean method, which works even with a single partly entangled pair, involves discarding the extra probability of the larger term in the entangled state, leaving a perfectly entangled state. The paper also discusses the efficiency of entanglement concentration and its relation to quantum data compression. While quantum data compression can be used to approximate entanglement concentration, it is not as effective as the Schmidt projection method. The paper shows that two-sided quantum data compression does not work as a method of entanglement concentration, as it fails to produce maximally entangled states. Conversely, entanglement concentration by the Schmidt projection method necessarily sacrifices fidelity to the original state in order to produce a maximally entangled output. The paper concludes that entanglement concentration is a crucial process in quantum information theory, allowing the transformation of partly-entangled states into maximally entangled states. The Schmidt projection method is the most efficient method for this task, with the yield of singlets approaching the entropy of entanglement of the initial state. The paper also discusses the limitations of entanglement measures for mixed states and presents examples of entangled mixed states, such as the Werner state.