Diastereoisomer introduction

Stereoisomers have identical composition and atom-to-atom bonding sequence, but they differ in the arrangement of the atoms in space. 

Enantiomers are stereoisomers that are nonsuperimposable mirror images of one another.

For compounds with two stereogenic centres, the enantiomer has the opposite configuration at all stereogenic centres.

For compounds with two stereogenic centres, R R and S S are enantiomers.

Example: trans-1,2-dichlorocyclohexane


A word of warning:  In order for a compound with two stereogenic centres to exist as enantiomers, the compound MUST be asymmetric (no symmetry planes!).

Examplecis-1,2-dichlorohexane is an example of a compound that has a symmetry plane, and its mirror images are superimposable.
 
 

Note that the configurations of the stereogenic centres on opposite sides of the mirror plane are opposite.
 
Diastereoisomers are stereoisomers that are NOT mirror images of one another.
Diastereoisomers have some (but not all) stereogenic centres with the opposite configuration.
R S and R R are diastereoisomers.
R S and S S are diastereoisomers.

cis-1,2-dichlorocyclohexane and either of the enantiomers are trans-1,2-dichlorocyclonexane are diastereomers.

Some useful general observations from the above diagrams:
Swapping two groups at a stereogenic centre inverts its configuration.
Swapping H and Cl converts R to S or S to R above.

For a compound with two stereogenic centres
If the groups at both stereogenic centres are the same, the R,S and S,R compounds are identical (as above).