The peptidoglycan monomers are synthesized in the cytosol and are then attached to a membrane carrier bactoprenol.  Bactoprenol transports peptidoglycan monomers across the cell membrane where they are inserted into the existing peptidoglycan.
# In the first step of peptidoglycan synthesis, glutamine, which is an amino acid, donates an amino group to a sugar, fructose 6-phosphate. This reaction, catalyzed by EC 2.6.1.16 (GlmS), turns fructose 6-phosphate into glucosamine-6-phosphate.
# In step two, an acetyl group is transferred from acetyl CoA to the amino group on the glucosamine-6-phosphate creating N-acetyl-glucosamine-6-phosphate. This reaction is EC 5.4.2.10, catalyzed by GlmM.
# In step three of the synthesis process, the N-acetyl-glucosamine-6-phosphate is isomerized, which will change N-acetyl-glucosamine-6-phosphate to N-acetyl-glucosamine-1-phosphate. This is EC 2.3.1.157, catalyzed by GlmU.
# In step 4, the N-acetyl-glucosamine-1-phosphate, which is now a monophosphate, attacks UTP.  Uridine triphosphate, which is a pyrimidine nucleotide, has the ability to act as an energy source. In this particular reaction, after the monophosphate has attacked the UTP, an inorganic pyrophosphate is given off and is replaced by the monophosphate, creating UDP-N-acetylglucosamine (2,4). (When UDP is used as an energy source, it gives off an inorganic phosphate.) This initial stage, is used to create the precursor for the NAG in peptidoglycan. This is EC 2.7.7.23, also catalyzed by GlmU, which is a bifunctional enzyme.
# In step 5, some of the UDP-N-acetylglucosamine (UDP-GlcNAc) is converted to UDP-MurNAc (UDP-N-acetylmuramic acid) by the addition of a lactyl group to the glucosamine. Also in this reaction, the C3 hydroxyl group will remove a phosphate from the alpha carbon of phosphoenolpyruvate. This creates what is called an enol derivative. EC 2.5.1.7, catalyzed by MurA.
# In step 6, the enol is reduced to a "lactyl moiety" by NADPH in step six. EC 1.3.1.98, catalyzed by MurB.
# In step 7, the UDP–MurNAc is converted to UDP-MurNAc pentapeptide by the addition of five amino acids, usually including the dipeptide -alanyl--alanine. This is a string of three reactions: EC 6.3.2.8 by MurC, EC 6.3.2.9 by MurD, and EC 6.3.2.13 by MurE.
Each of these reactions requires the energy source ATP.  This is all referred to as Stage one.
Stage two occurs in the cytoplasmic membrane. It is in the membrane where a lipid carrier called bactoprenol carries peptidoglycan precursors through the cell membrane.
# Undecaprenyl phosphate will attack the UDP-MurNAc penta, creating a PP-MurNac penta, which is now a lipid (lipid I). EC 2.7.8.13 by MraY.
# UDP-GlcNAc is then transported to MurNAc, creating Lipid-PP-MurNAc penta-GlcNAc (lipid II), a disaccharide, also a precursor to peptidoglycan. EC 2.4.1.227 by MurG.
# Lipid II is transported across the membrane by flippase (MurJ), a discovery made in 2014 after decades of searching. Once it is there, it is added to the growing glycan chain by the enzyme peptidoglycan glycosyltransferase (GTase, EC 2.4.1.129). This reaction is known as transglycosylation.  In the reaction, the hydroxyl group of the GlcNAc will attach to the MurNAc in the glycan, which will displace the lipid-PP from the glycan chain.
# In a final step, the DD-transpeptidase (TPase, EC 3.4.16.4) crosslinks individual glycan chains. This protein is also known as the penicillin-binding protein. Some versions of the enzyme also performs the glycosyltransferase function, while others leave the job to a separate enzyme.