It's just over 5 years old, but 'A Primer of Genome Science, 3rd Edition' by Gibson and Muse (link here) covers a lot of the needed basics. I used this as the major reference in a Senior Graduate Seminar I taught last Fall for CS/Bioinformatics students who lacked a biology background and it worked fairly well for the first two thirds of the course.

Attwood, Teresa K.; Higgs, Paul (2005). Bioinformatics And Molecular Evolution. Cambridge, MA: Blackwell Publishers. ISBN 1-4051-0683-2.

For genomics, I would recommend Genome 3 from T. A. Brown

http://www.garlandscience.com/product/isbn/9780815341383

Part 1: Studying Genomes

1. Genomes, Transcriptomes and Proteomes
2. Studying DNA
3. Mapping Genomes
4. Sequencing Genomes
5. Understanding a Genome Sequence
6. Understanding How a Genome Functions

Part 2: Genome Anatomies

7. Eukaryotic Nuclear Genomes
8. Genomes of Prokaryotes and Eukaryotic Organelles
9. Virus Genomes and Mobile Genetic Elements

Part 3: How Genomes Function

10. Accessing the Genome
11. Assembly of the Transcription Initiation Complex
12. Synthesis and Processing of RNA
13. Synthesis and Processing of the Proteome
14. Regulation of Genome Activity

Part 4: How Genomes Replicate and Evolve

15. Genome Replication
16. Mutations and DNA Repair
17. Recombination
18. How Genomes Evolve
19. Molecular Phylogenetics