UFO: Afterlight wiki
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This article contains advice on a strategy for starting the game. 

Every game starts out with your base in Stuttgart, the capital of Central Europe, and one province with resources. Since this is also part of Central Europe you are automatically collecting resource income from it.   

Start   exploring  neighbouring territories within Central  Europe, as you can collect income from these without having to build tracks.When you need to expand there are a few bases very close by.  Paris, in North East France contains a base, which is adjacent to Stuttgart.   North of Paris is England, which as well as being a base is also your first base with sea-lanes available.  From here you can choose to link Spain, if you want to stay in Europe, or expand over to New York and South America.  I advise that you stick to Europe until you have that established, as the Laputa is quite slow moving, and you don’t want to keep jumping the Atlantic to do missions. Using this strategy you can link 4 bases with only 3 tracks.   Capture the resource provinces that they are linked to and you have the start of a strong economy. 

Build weapons labs to research human weapons, and have weapons factories and ordnance factories churning out weapons, armour and ammo for your soldiers.  Use weapons that you find in missions, but bear in mind you only have limited ammo for them until they are researched.  Try to equip your squad with a variety of weapons, that way they won’t all run out of ammo at the same time, and will all have different strengths and weaknesses. 

For instance a shotgun does loads of damage, but it only has a short range.  Therefore give it to someone who is good with the weapon (Short Range skill) and is fast, so they can get close to the target quickly before they are shot to pieces.

Give everyone a knife and a med-pack.  There should be enough to give most of your squad one each, but if not give them to the soldiers who can make best use of them. No point giving a med-pack to someone with Awful Medical skill, when you have a soldier with Good Medical.  Also move the weapons around before the first mission,as they haven’t been given to the best people.  As a last resort knives can be used to fight with, but are best used to finish off unconscious enemies on the floor, as it saves ammo.

When you go on a mission move slowly and carefully across the map.  When you spot an enemy you will probably need to focus all your firepower on it to bring it down quickly.  If you encounter a group of enemies it is better to focus your shooting on just one target early on.  This way you will reduce the number of guns shooting at you faster than spreading your shots between them.

Research is a very important part of the game, as it enables you to discover and produce new and more powerful weapons.  Multiple labs will increase the speed of research, and they should never be sitting idle until there is nothing left to research. And be careful of Laputan research. Some of them can only done on Laputan lab, not on ground labs, and the obvious restraint on your progress quickly through phases of game.

Also, keep in mind the relation between weapons and researchs. Some type items require a research before being able to use, and if you have a lot of that type, that research can bring more utility than the others.