Tannins occur naturally in the skins of wine grapes and are the compound that creates a drying sensation in your mouth as you drink.  People that are sensitive (or even allergic) to this sensation as well as that of bitterness can be put off red wines entirely for fear of encountering these tannins.  However, there is absolutely no need, because depending on how the wine was made and what grapes were utilized, you can easily find a red wine to enjoy that is low in tannins.

Look to varietals with more delicate skins.  Because red wine receives the majority of its tannins from the grape’s skins, where it also receives its colour, the thinner the skin, the less tannin it has to impart in the wine.  Pinot Noir is the go-to in this category, delivering light, fresh flavours with relatively low tannins.  The classical home of Pinot Noir is of course Burgundy, and a suitable starting point comes in the form of the Olivier Leflaive Bourgogne Pinot Noir 2015, £17.95:
From 25 year old vines this is a blend of different vineyards from Cote de Beaune, Cote Chalonaise, les Hauts Cotes de Beaune and Cote de Nuits.  10% is aged in oak barrels and the rest in stainless steel.   A fruity pinot noir with charm and finesse, ideal with charcuterie and hard cheese such as Gouda.
Increasingly New Zealand is competing with Burgundy in the production of quality Pinot Noir, with Marlborough’s Forrest Estate Pinot Noir 2013, £14.50 offering great value for money in their 2013 vintage offering:
"Rich fruit tinged with cocoa and lavender, this wine is poised and cheerful.  It has a slightly earthy nose underneath the pretty aromatics, with delicate cranberries and cherries on a sweet-savoury palate, then hints of coffee on the finish. 91 Points." (Decanter Magazine - New Zealand Pinot Noir Tasting, August 2016).
Gamay is also appropriate here, a grape that also hails from Burgundy and is more often found under the name of the region it calls home, Beaujolais.  This is represented excellently in the Château de Beauregard Fleurie Classic 2014, £16.50:
The Fleurie of Château de Beauregard is among the most textured of the Fleurie appellation reminiscent of the style of the neighbouring Moulin à Vent.  The nose reveals floral aromas (iris, rose petal and violet), dry hay and red fruit. The palate shows flavours of strawberry and blackcurrant enveloped in a velvety smooth fleshiness leading to a long satisfying finish. 
Also falling into this category are the Dolcetto and Barbera grape varietals of Piedmont, Italy.  These wines are light, bright and refreshing, delivering flavours of fresh red berries along with smooth, supple tannins and lie in stark contrast to their geographical counterparts, Barolo and Barbaresco.  Appropriate and accessible examples of both come in the form of the Pira Luigi Dolcetto d'Alba 2015, £12.69:
Meaning ‘little sweet one’, this grape is of great importance to the Piedmontese and is perfectly suited to the north-west of Italy in both climate and soil. It is matured in steel tanks for 8 to 9 months which contributes to its fresh and fruity cherry and almond character.  It is a flavourful wine redolent of dark fruit in a soft style that shows great richness.  It is very well-balanced with a long and complex finish.
 …and the Pico Maccario Lavignone Barbera D'Asti 2015, £11.99:
This is 100% Barbera and is a delightful glass of wine showing all the typicity of the grape. Aromas of cherry, plum and red berries. On the palate it is very fruit forward with good acidity and balanced tannins. Ideal with meaty fish, duck, game and pork. The wine’s earthy flavours will nicely compliment any dish containing herbs and mushrooms. Served slightly chilled, it can also be paired with spicy foods such as barbeque or Indian curry. 
Tannins in wine can also arise as a result of oak ageing.  Often the newer the oak, the more likely it is to impart this mouth-drying compound into the wine which is the practice in typically bigger reds such as Cabernet, Merlot or Syrah, which are already full of their own natural tannins, so by avoiding the wines already known for being higher in tannins, you should be alright.  As usual, if you have any concerns regarding tannins in wine or would like to be pointed in the direction of something potentially more suited to your palate do not hesitate to ask us.