Normalisation of practise database
Your breakup of the table is largely correct.  There is three tangible objects, a book, the author, and the publisher.  Each of these needs a table, we also need a table to store the relationship between Authors and Books and Publishers and Books as these relationships are many to many.

Books 

ISBN (primary key)
Title
Price 


Authors

AuId (primary key)
AuName 
AuPhone 


Publishers

PubId (primary key)
PubName
PubPhone


Authors to Books

AuBId (primary key)
AuId (composite key)
ISBN (composite key)


Publishers to Books

PubBId (primary key)
PubId (composite key)
ISBN (composite key)


You could just use the composite keys instead of having an explicit primary key on the last two tables that define the many-to-many relationships.

Edit:

When I say composite key I mean if a primary key exists that it is an alternate unique key made of multiple columns.  If there is no other primary key defined then the primary key would be defined as both columns, i.e. PubId and ISBN.  There are both pros and cons for doing using a composite key as the primary key, people have different takes on the best option.

There is no reason to explicitly store the libary table with the table structure above, all the information is already stored.  If absolutely necessary I would think that the ISBN is unique, if not you could as mentioned add a primary key column like serialno which maintain integrity.