MacBook does not mount, does not boot, does not read drive
The GUID partition table is a mess. 

Just to explain all partitions:


i = 1 EFI partition
i = 2 main OS X volume (wrong partition type)
i = 3 Recovery HD (wrong partition type)
i = 4 Windows partition (wrong partition type)
i = 5,7 Linux partitions
i = 6  Linux Swap partition


I would do the following after booting to Internet Recovery HD:


First you have to unmount disk0 and get the gpt table:

diskutil umountDisk /dev/disk0
gpt -r show /dev/disk0

Open Utilities->Terminal and remove the two Linux partitions (5,7) and the Linux Swap partition (6) with:

gpt remove -i 7 /dev/disk0
diskutil umountDisk /dev/disk0
gpt remove -i 6 /dev/disk0
diskutil umountDisk /dev/disk0
gpt remove -i 5 /dev/disk0

Remove the Windows partition (marked as an Apple HFS+ partition)

diskutil umountDisk /dev/disk0
gpt remove -i 4 /dev/disk0

Remove and properly re-add the Recovery HD: 

diskutil umountDisk /dev/disk0
gpt remove -i 3 /dev/disk0
gpt add -b 176870968 -i 3 -s 1269536 -t 426F6F74-0000-11AA-AA11-00306543ECAC /dev/disk0

Remove and properly re-add the OS X partition:

diskutil umountDisk /dev/disk0
gpt remove -i 2 /dev/disk0
gpt add -b 409640 -i 2 -s 176461328 -t 48465300-0000-11AA-AA11-00306543ECAC /dev/disk0


the type of the partition may also be 53746F72-6167-11AA-AA11-00306543ECAC (CoreStorage). With on-board tool it's impossible to determine the correct partition type.
Verify disk0 and disk0s2:

diskutil verifyDisk /dev/disk0
diskutil verifyVolume /dev/disk0s2


If you get errors you may consider replacing the default partition type of disk0s2 by a CoreStorage volume:

diskutil umountDisk /dev/disk0
gpt remove -i 2 /dev/disk0
gpt add -b 409640 -i 2 -s 176461328 -t 53746F72-6167-11AA-AA11-00306543ECAC /dev/disk0


Enter diskutil cs list. If you get No CoreStorage logical volume groups found as result repeat step 5 and continue with the diskutil verifyDisk... and diskutil repairDisk... steps below. If the diskutil cs list reveals a CoreStorage Volume Group check if it is encrypted: Logical Volume Family -> Encryption: locked. Unlock the volume with: diskutil cs unlockVolume lvUUID with lvUUID: the UUID of the Logical Volume and entering your passphrase.

Verify disk0 and disk0s2 again:

diskutil verifyDisk /dev/disk0
diskutil verifyVolume /dev/disk0s2


If you still get errors try to repair disk0 and disk0s2:

diskutil repairDisk /dev/disk0
diskutil repairVolume /dev/disk0s2

Quit Terminal by entering exit and try to reboot to your main OS X volume


If you get an error saying disk0 Resource busy... you have to unmount disk0 again with diskutil umountDisk /dev/disk0.