refer to wikipedia---
1NF(first normal form):
1. There's no top-to-bottom ordering to the rows.
2. There's no left-to-right ordering to the columns.
3. There are no duplicate rows.
4. Every row-and-column intersection contains exactly one value from the applicable domain (and nothing else).
5. All columns are regular [i.e. rows have no hidden components such as row IDs, object IDs, or hidden timestamps].
2NF(second normal form):
if and only if it is in 1NF and every non-prime attribute of the table is dependent on the whole of a candidate key.
A non-prime attribute of a table is an attribute that is not a part of any candidate key of the table.
Not all 2NF tables are free from update anomalies.
A table for which there are no partial functional dependencies on the primary key is typically, but not always, in 2NF.
3NF(third normal form):
The relation R (table) is in 2NF
Every non-prime attribute of R is non-transitively dependent (i.e. directly dependent) on every superkey of R.
A transitive dependency is a functional dependency in which X → Z (X determines Z) indirectly, by virtue of X → Y and Y → Z (where it is not the case that Y → X).
Requiring existence of "the key" ensures that the table is in 1NF; requiring that non-key attributes be dependent on "the whole key" ensures 2NF; further requiring that non-key attributes be dependent on "nothing but the key" ensures 3NF.
BCNF(3.5 normal form):
If a relational schema is in BCNF then all redundancy based on functional dependency has been removed, although other types of redundancy may still exist. A relational schema R is in Boyce–Codd normal form if and only if for every one of its dependencies X → Y, at least one of the following conditions hold:[4]
- X → Y is a trivial functional dependency (Y ⊆ X)
- X is a superkey for schema R
A 3NF table which does not have multiple overlapping candidate keys is guaranteed to be in BCNF. Depending on what its functional dependencies are, a 3NF table with two or more overlapping candidate keys may or may not be in BCNF
3NF：只消除非主属性对主属性的传递依赖；
BCNF：消除所有属性对主属性的传递依赖。
4NF(forth normal form)：
A Table is in 4NF if and only if, for every one of its non-trivial multivalued dependencies X 
Y, X is a superkey—that is, X is either a candidate key or a superset thereof.
A trivial multivalued dependency X Y is one where either Y is a subset of X, or X and Y together form the whole set of attributes of the relation.