If no sentient being exists, for whom is there compassion? 'A Guide to the Bodhisattva Way of Life' by Santideva Quoted below is from 'A Guide to the Bodhisattva Way of Life' by Santideva, Chapter IX: The Perfection of Wisdom. I'm struggling to follow the line of thought, can someone please decipher what it means. 

This is what I deduce reading it and It really is incomprehensible to my feeble mind.  


Sentient beings do not exist
For one to be compassionate he has to be deluded to believe that sentient beings exist.
Compassion itself is a delusion
One should remain deluded to alleviate the nonexisting suffering of nonexisting sentient beings.


How can all this be true? 

Please note I'm writing bluntly because I want to understand what it means not because of lack of respect for Santideva work, far from it his book is always in my heart... it just that I can't get through chapter 9 :/ 


  
  [Qualm:] If no sentient being exists, for whom is there compassion?  [Madhyamika:] For one who is imagined through delusion,
  which is accepted for the sake of the task.
  [Qualm:] If there is no sentient being, whose is the task?  [Madhyamika:] True. The effort, too, is due to delusion.
  Never­theless, in order to alleviate suffering, delusion with regard
  to  one's task is not averted
First, you have to keep in mind that Shantideva's work is versified. This implies that it is not always technically accurate, because words are missing for the sake of poetry. For instance, we will read "sentient beings do not exist" as "sentient beings do not exist inherently" implying "but they do exist conventionally." What does not exist is a mode of existence.

Second, Shantideva was a Prasangika. This is his view of emptiness that neither persons nor phenomena exist inherently. They do exist conventionally. Prasangika also posit that conventional valid cognizers in the continuum of ordinary beings are valid with regard to the entity of the thing, but mistaken with regard to the mode of existence of said things. This all helps you understand that we do not negate conventions.

Third, Gyaltsab Je wrote a Prasangika commentary to Shantideva. He explains verse 9.75 as follows:


  Gyaltsab Je: Realist: If there is absolutely no inherently existing
  person, then, as there is no focal object for compassion, for whom
  should one practice meditation on compassion? Madhyamaka: If there is
  no inherently existing person, then it follows there is no such fault
  that the focal object of compassion is non-existent, because that
  nominally existing sentient being, labelled by mental darkness, which
  is accepted for the purpose of achieving the result of liberation, is
  valid to be the focal object of compassion.


While part of his commentary on verse 9.76 says:


  The opponent says that if sentient beings do not exist inherently they
  do not exist at all. The question is that if sentient beings do not
  exist, who would experience the result of meditation on compassion
  that is buddhahood? It is clear that the object of observation as well
  as the result of the meditation on compassion do not exist truly, but
  the problem as posited by the opponent does not exist for us, in that
  sentient beings still exist conventionally, and therefore
  conventionally it makes sense to meditate on compassion.


Now, to answer your questions more directly:

1) Sentient beings do not exist
They do not exist inherently (or truly), they do exist conventionally. A valid eye consciousness apprehending a person is valid with regard to the entity of the thing. Compassion towards a person is valid with regard to the entity of the thing as well. Compassion towards a unicorn, however, is not.

2)For one to be compassionate he has to be deluded to believe that sentient beings exist.
No. For one to be compassionate, he has to have some sort of insight into the four noble truths. Also, he who believes that sentient beings are utterly non-existent is deluded. So is he who believes they exist inherently (which is the whole topic here).

3)Compassion itself is a delusion
It is not, because a delusion is never valid with regard to the entity of the thing. For instance, anger does not engage its object correctly. The object [of engagement] of anger is as non-existent as a unicorn. In addition, delusions take away the peace of the mind (it's their definition) and superimpose.

4)One should remain deluded to alleviate the nonexisting suffering of nonexisting sentient beings.
This is not the case, since the conventionally existent buddhas do alleviate the conventionally existing suffering of conventionally existent sentient beings.



Non-versified books you can read on the topic are:

1. Commentary on Shantiva


Gyaltsab Dharma Rinchen, The Entrance for the Children of the Conquerors, A Commentary on Shantideva’s Introduction to the Actions of Bodhisattvas


2. Madhyamika


Elizabeth Napper, Dependent‑Arising and Emptiness


3. Special Insight


Je Tsongkhapa, Lam Rim Chen Mo, Volume 3, Part 2
Je Tsongkhapa, Middle Length Lam Rim, Chapter Five
Guy Newland, Introduction to Emptiness
Guy Newland, The two truths
Jeffrey Hopkins, Tsongkhapa's Final Exposition of Wisdom
Khedrup Je - A Dose of Emptiness