Polyethylenimine (PEI) or polyaziridine is a polymer with repeating units composed of the amine group and two carbon aliphatic CH_2CH_2 spacers. Linear polyethyleneimines contain all secondary amines, in contrast to branched PEIs which contain primary, secondary and tertiary amino groups. Totally branched, dendrimeric forms were also reported. PEI is produced on an industrial scale and finds many applications usually derived from its polycationic character. The linear PEI is a semi-crystalline solid at room temperature while branched PEI is a fully amorphous polymer existing as a liquid at all molecular weights. Linear polyethyleneimine is soluble in hot water, at low pH, in methanol, ethanol, or chloroform. It is insoluble in cold water, benzene, ethyl ether, and acetone. Linear polyethyleneimine has a melting point of around 67 °C. Both linear and branched polyethyleneimine can be stored at room temperature. Linear polyethyleneimine is able to form cryogels upon freezing and subsequent thawing of its aqueous solutions. Branched PEI can be synthesized by the ring opening polymerization of aziridine. Depending on the reaction conditions different degree of branching can be achieved. Linear PEI is available by post-modification of other polymers like poly(2-oxazolines) or N-substituted polyaziridines. Linear PEI was synthesised by the hydrolysis of poly(2-ethyl-2-oxazoline) and sold as jetPEI. The current generation in-vivo-jetPEI uses bespoke poly(2-ethyl-2-oxazoline) polymers as precursors. Polyethyleneimine finds many applications in products like: detergents, adhesives, water treatment agents and cosmetics. Owing to its ability to modify the surface of cellulose fibres, PEI is employed as a wet-strength agent in the paper-making process. It is also used as flocculating agent with silica sols and as a chelating agent with the ability to complex metal ions such as zinc and zirconium. There are also other highly specialized PEI applications: PEI has a number of uses in laboratory biology, especially tissue culture, but is also toxic to cells if used in excess.