I want to lay Granite tiles on my kitchen flooring and walls and I heard that because granite tiles are heavy, they may fall off with the passage of time, if proper and strong "Underlay" adhesive compound is not applied.
Now I do not know which is the best and most strong underlay for marble and granite tiles?

Not so sound goofy, but what does the manufacture supplier speck in the application to warranty the product.
The strongest underlay for tiles is a concrete slab floor or the cement board durock.
Now the next question if you are going on joist how big are the joist and there centers to carry the granite load the durock load and the person(s) standing on that?
The walls should be glued and screwed durock cement boards and that's the most solid and strongest wall you can get to set tile on.
The tile floor equation is the tiles sitting flat per piece and full spread. The sub floor has to be stiff and strong enough also.
Check this site on the cement board on kitchen floors
All grout needs sealed especially in a kitchen

http://www.tileshop.com/DIY/index.aspx

Signed 21 Boat

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Great answer 21boat.

For your kitchen floor, ensure that you follow guidelines for joist spacing. Your existing floor should have a 3/4 in of subfloor and possibly a 1/2 of plywood underlayment. Plywood should be replaced with a 1/2 in cement board underlayment follow manufacturer instructions for fasteners and spacing.

Cement board should be used on the wall with the correct adhesive material.

Go to LATICRETE® International > Home or www.mapei.com to get information of adhesive and grout systems to properly install the granite.

Good Luck

Not sure what your walls and floor material is so its not possible to talk about underlayment, you might not need any. The best adhesive for tile on any floor or wall that is not concrete is a modified thinset. If you want to also discuss underlaymnent you need to tells us about your wall and floor material.

First of all I would like to thank all of you good guys in extending your helping hands towards my question.

I have basement with all concrete walls and I want to install granite at least for a border around and hopefully on the floor as well, if price doest not kill me!

Then I have kitchen tops, the floor and then come the bath rooms, at least, the floors of the bath room. My house doest not have any wood construction, its all bricks, cement and plaster.

The trouble is I love granites and if it not hugely expensive then I would run for it.

Many Thanks for your input