Isomers are molecules with the same chemical formula but difference in connectivity or spatial arrangement.
Conformational isomers
Conformational isomers are identical molecules that have undergone some kind of bond rotation. They are sometimes called rotational isomers for this reason.
The image below shows two types of rotation. On the left, we can see the Newman projections of 1,2-dichloroethane as it rotates; on the right, we can see the chair flip of a disubstituted cyclohexane: 
Conformational isomers
Constitutional isomers
Constitutional isomers have the same number of atoms but different structural connectivity (aka chemical structure). The difference in connectivity can be simply moving a functional group around or it can be forming a ring instead of a straight chain.
Bromohexane and pentene constitutional isomers
It’s easy to see that the molecules on the left have the same chemical formula since they look similar, but the molecules on the right can be a bit tricky. A handy way to tell at a glance if molecules have the same chemical formula is to determine a molecule’s index of hydrogen deficiency (AKA degrees of unsaturation).
How do you tell the difference between constitutional isomers vs resonance structures? Remember that atoms move in constitutional isomers but atoms never move in resonance structures.
Stereoisomerism
Stereoisomers are compounds that have the same chemical formula, the same atomic connectivity, and different spatial arrangement that cannot be achieved through rotation. They’ve got non-superimposable mirror images. There are a few types of stereoisomers:
Enantiomers
A pair of enantiomers’ chiral centers are all opposite with respect to the R & S configuration. If the molecule only has one chiral center, it must go from R to S or vice-versa; if the molecule has more than one chiral center, all must swap from R to S or vice-versa. Enantiomers tend to have similar properties like boiling point.
2-bromohexane-enantiomers
Diastereomers
There are two types of diastereomers: one type is a pair of molecules that have multiple chiral centers; the second type is a pair of molecules with opposite cis or trans connectivity across a pi-bond.
The first type requires some but not all of the chiral centers to swap R & S. Let’s compare what that looks like with enantiomers:
Enantiomers vs diastereomers
Notice that in the enantiomers, both chiral centers swapped from R to S or vice-versa; in the box on the right, the diastereomers, not all of the chiral centers swapped. Even if you’ve got 100 chiral centers but only 99 are flipped from one molecule to the other, they’re diastereomers.
The second type has a pi-bond that can exist either as a cis or trans isomer. The pi-bond does not allow rotation due to its orbital overlap, so molecules are locked as cis or trans. Cis/trans isomers used to be called geometric isomers, but that term has fallen out of fashion. 
2-pentene diastereomers
Meso
Meso compounds are kind of tricky, but we’ve got a nice method to figure them out! Basically, they’re overall-achiral molecules with at least two chiral centers and an internal plane of symmetry. Sounds weird, right? Even weirder, they’re their own enantiomers. All you need to do to is rotate them to see it. This property arises from their symmetry with respect to atomic connectivity.
Meso cyclohexanediol
Atropisomers
Atropisomers are molecules that are locked into a specific orientation through steric hindrance. In other words, they can’t rotate to another conformation. They're chiral, non-superimposable molecules with no chiral centers. Notice that this biphenyl is locked into position because of their four substituents; the groups would bump into each other, so rotation is impossible. They cannot be interconverted.
Biphenyl atropisomers
