Given the following unnormalized relation representing a library database:

Books $($Book$\_$ID$,$ Title, Author, Genre, Publisher, Publication$\_$Year, ISBN, Price$)$

a$)$ Define normalization in the context of database management systems $($DBMS$).$ Explain why normalization is essential for database design.

b$)$ Normalize this relation into First Normal Form $(1$NF$),$ Second Normal Form $(2$NF$),$ Third Normal Form $(3$NF$)$ and Boyce$-$Codd Normal Form $($BCNF$).$

c$)$ For each normalization step $(1$NF$,2$NF$,3$NF$,$ BCNF$)$ performed in Part $($b$),$ explain the specific functional dependencies present in the original relation and how they are addressed through normalization.

d$)$ Discuss the advantages and potential drawbacks of achieving higher normal forms $(3$NF and BCNF$)$ compared to lower normal forms $(1$NF and $2$NF$)$ in terms of database design, querying efficiency, and data integrity.