For fatty acid analysis, you may use FAME (derivetization) method or free fatty acid analysis using Caviezel® method (rapid method). For triglyceride analysis , you may see IUPAC protocols (see links below) or AOCS standard methods (Official Methods and Recommended Practices of the AOCS). Recommended protocols you may see in the following links: 

http://onlinelibrary.wiley.com/doi/10.1002/(SICI)1438-9312(200002)102:2%3C154::AID-EJLT154%3E3.0.CO;2-L/abstract;jsessionid=083D58A9BBE4084512C2B8972B16B6AF.f01t02

http://old.iupac.org/publications/books/ISBN0632033371_compress.pdf 

Hi, Mr Eddington Gororo, for FAME analysis; you can go through my article once. Here I have mentioned the standardized protocol for it. 

please get the attachment below...

Article Fatty acids as biomarkers of microalgae

For previous separation of lipid classes, I would rather go for SPE than for TLC. There are plenty of protocols depending on which type of lipid classes are you interested in. Find two below for major lipid classes (non-polar lipids -mainly tryglycerides-,  free fatty acids and polar lipids -mainly phospholipids-) and for phospholipid classes:

https://www.researchgate.net/publication/220036753_Improvement_of_a_solid_phase_extraction_method_for_analysis_of_lipid_fractions_in_muscle_foods

https://www.researchgate.net/publication/220036718_Improvement_of_a_solid_phase_extraction_method_for_separation_of_animal_muscle_phospholipid_classes

For the subsequent analysis of fatty acid composition, there are plenty of derivatization methods aimed to produce the methyl esters derivatives. Perhaps the Boron trifluoride method is the most common one, but there are others that work also quite good:

http://www.cyberlipid.org/fattyt/fatt0001.htm#2

Article Improvement of a solid phase extraction method for analysis ...

Article Improvement of solid phase extraction method for separation ...

Triglycerides composition can be determined without derivatization by GC-FID analysis after their dissolution in n-heane or similar organic solvent by using a high temperature column (I suggest RTX-65 TG HT, l=30 m; i.d.=0.25 mm; f.t.=0.25 micron). Fatty acid composition can be determined after derivatization of triglycerides by using KOH 2N in methanol added to sample dissolved in n-hexane. After 2 minutes of vigorous agitation the two phases will separate; inject 1 microliter of n-hexane (upper phase) into GC-FID. If you need other information please visit my personal page and you will find many papers dealing with this topic.

This is a rather straight forward issue and will be focused mainly on the analysis of acyl chains in phospholipid chains.  Because sperm lipids contain a fair bit of DHA (22:6n-3), you want to avoid highly oxidative processes such as BF3.  A milder procedure such as KOH in methanol will work well with good recovery.  The key is to use dry methanol to avoid free acid formation.

For analysis, we have always used a SP-2330 column (30 m capillary column) with very good results.  Should also work well for you and GLC would be the method of choice for this analysis over more technically difficult analysis.

I would recommend separating the major PL via either HPLC or via TLC and assessing the lipid composition of the individual PL.  This will make the study more attractive to journals over a simple, bulk PL analysis.

For sample extraction, I would avoid CHCl3 methods and stick to Norm Radin's single phase extraction with hexane:2-propanol (3:2 by vol).  This is a more PUFA friendly process even if you add some BHT. 

Our lab's protocols are published in multiple papers and books over the years.  Some of these are found in Lipid Mediated Signal Transduction by Rosenberger and Murphy. 

There are some good suggestions above.  However it can be difficult to detect triglycerides with GC-MS as these are large molecules and often at the upper mass limit for a quadropole mass spec.  You also need a high temperature column as the top oven temperature will need to be high to make sure the larger molecules elute.  GC-MS is very good for free fatty acids either methylated, as above, and separated on a general type of column (such as DB5) or a specialised longer column specifically designed for FAMES.  I look at degraded fats from archaeological materials and usually start with BSTFA derivatised samples as these can give more structural information if hydroxy fatty acids are present for example.  This derivatisation method has the disadvantage of being reversible so has to be carried out shortly before analysis and with completely dry samples.  It does not give such good results for separating PUFAs/MUFAs as methylation.  It can be done after methylation for the structural information as the hydroxyl groups are unaffected by methylation and can  subsequently be silylated to provide that fine detail.

Thank you colleagues for your answers. They are quite helpful. I will look at all the protocols you recommended and use the one most feasible in our circumstances