The paper discusses the process of concentrating partial entanglement by local operations and classical communication. Two separated observers, Alice and Bob, start with $n$ pairs of particles in partially entangled pure states. They can use local actions to concentrate this entanglement into a smaller number of maximally entangled pairs, such as Einstein-Podolsky-Rosen (EPR) singlets, while asymptotically conserving the entropy of entanglement. Conversely, any pure or mixed entangled state of two systems can be prepared from a supply of singlets using local operations and classical communication. The authors introduce the concept of "entanglement concentration" and describe a method called Schmidt projection, which involves projecting the joint state of $n$ pairs onto a subspace spanned by states with a common Schmidt coefficient. They also discuss the efficiency of this method and compare it with another method called the Procrustean method. The paper further explores the relationship between entanglement concentration and quantum data compression, showing that while these techniques are complementary, they cannot be used interchangeably. Finally, the authors discuss the limitations and implications of entanglement concentration and dilution for mixed states, highlighting the lack of a simple entanglement measure for such states.The paper discusses the process of concentrating partial entanglement by local operations and classical communication. Two separated observers, Alice and Bob, start with $n$ pairs of particles in partially entangled pure states. They can use local actions to concentrate this entanglement into a smaller number of maximally entangled pairs, such as Einstein-Podolsky-Rosen (EPR) singlets, while asymptotically conserving the entropy of entanglement. Conversely, any pure or mixed entangled state of two systems can be prepared from a supply of singlets using local operations and classical communication. The authors introduce the concept of "entanglement concentration" and describe a method called Schmidt projection, which involves projecting the joint state of $n$ pairs onto a subspace spanned by states with a common Schmidt coefficient. They also discuss the efficiency of this method and compare it with another method called the Procrustean method. The paper further explores the relationship between entanglement concentration and quantum data compression, showing that while these techniques are complementary, they cannot be used interchangeably. Finally, the authors discuss the limitations and implications of entanglement concentration and dilution for mixed states, highlighting the lack of a simple entanglement measure for such states.