Être en train de is a handy French expression that describes an event in progress. It's always followed by an infinitive and is often translated as "to be in the process of" or "to be in the middle of":

Donc, je suis en deuxième année là;

So, I'm in my second year now;

je suis en train de... achever ma formation.

I'm in the process of... completing my training.

Caption 25, 4 Mains pour 1 Piano - Médaillon de Homard

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Là je suis en train de régler les meules pour que

Here I am in the middle of setting the millstones so that

le grain soit correctement écrasé.

the grain is crushed correctly.

Caption 4, Télé Lyon Métropole - Chaillé-les-Marais : Une biscuiterie 100 % familiale

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But just as often, être en train de can simply be translated with the present progressive tense ("to be doing," "to be making," etc.):

Donc, en ce moment, on est en train de faire des truffes cacao.

So, right now, we're making cocoa truffles.

Caption 7, Canadian Chocolate Seller - Chocolats

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In French, there is no difference between the present tense and the present progressive tense: on fait can mean both "we make" and "we are making." So the above example could also be written:

Donc, en ce moment, on fait des truffes cacao.
So, right now, we're making cocoa truffles. 

Être en train de emphasizes the fact that the activity is currently in progress (further emphasized above by en ce moment). In fact, "currently" is another possible translation of être en train de:

...je suis en train de travailler avec celui qui a fait 'Pulp Fiction',

...I'm currently working with the person who made 'Pulp Fiction,'

Caption 9, Melissa Mars - From Paris with Love

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You can also use être en train de to describe a continuing event in the past. In this case, it's synonymous with the imperfect tense: 

Quand j'ai fait cette photo, la baleine était en train de dormir.

When I took this picture, the whale was sleeping.

Caption 25, Le Journal - Sillonner & photographier les océans

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Quand j'ai fait cette photo, la baleine dormait.
When I took this picture, the whale was sleeping.

Here again, être en train de stresses the continuousness of the action: the whale was "in the process of" sleeping when the speaker took the picture. 

Être en cours de has the same meaning and function as être en train de, except it's usually followed by a noun instead of an infinitive:

Un immense chantier est en cours d'achèvement.

A huge construction project is being completed.

Caption 25, Voyage dans Paris - Cour de l'Industrie

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A final note: Make sure not to confuse en train with entrain, a noun meaning "enthusiasm" or "liveliness." Nous espérons que vous êtes en train d'étudier le français avec entrain! (We hope you're in the process of studying French with enthusiasm!)

We know you look to Yabla for language, not math, so apologies in advance to any arithmophobes out there. Yes, we're going to talk some numbers today, but you can count on us to go easy on you.

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Remember last time, when we talked about French adjectives that come before the noun they modify? Well, there's another category of adjectives that behave that way: numbers!

Parmi les expériences inoubliables des deux plongeurs...

Among the unforgettable experiences of the two divers...

Caption 20, Le Journal - Sillonner & photographier les océans

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In this video about Pierre and Laurent's beautiful underwater photography, you see an example where the adjective deux (two) comes before the noun plongeurs (divers). It's just like in English: "two divers."

And staying on the numerical track, when an adjective indicates a place in a series, like premier (first), prochain (next), or dernier (last), it should also be placed in front of the noun it qualifies. For example, le premier président (the first president).

If you would rather be on top of the water than underneath it, take a look at this lightning trip around the world in 50 days. Captain Bruno Peyron and his crew break Steve Fossett's record on their impressive catamaran.

Lorsque le jeune Bruno Peyron boucle le premier tour

When the young Bruno Peyron completed his first trip

du monde en équipage et sans escale...

around the world with a crew and without stopping...

Caption 17, Le Journal - Le record du Tour de Monde!

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Notice the adjective premier (first) that precedes the noun tour (trip), because premier indicates a place in a series (the first place).

However, be aware that prochain (next) and dernier (last) do not always precede the noun they modify. In fact, they follow the noun when they indicate a notion of time, as when they are used with a week, month, or year. For example: le mois prochain (next month).

We hear an example in the video about French youth up in arms against the loi Fillon designed to reform French education.

Trois mille à Lyon, ils étaient deux fois plus la semaine dernière.

Three thousand in Lyon, they were twice as many last week.

Caption 7, Le Journal - Manifestations des lycéens

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In this instance, the adjective dernière (last) is placed after the noun semaine (week) because it indicates an expression of time: the protest is simmering down a bit compared to the previous week.

Finally, one last number-related point: a tip on where to place an adjective if, after all you have learned from the Yabla lessons, you still aren't quite sure where the darn thing should go. It's easy math: count and compare the number of syllables in the two words, adjective and noun. Most often, the qualifying adjective is placed in front of the noun if the noun is composed of a greater number of syllables than the adjective. In other words, if the adjective is shorter, it goes in front.

Corrine, a young and charming French woman, shows us an example of this when talking about the merits of her hometown.

On a la chaleur, on a, euh...

We've got warm weather, we have, uh...

peut-être la pollution, mais on...

maybe pollution, but we...

en tout cas, on a de beaux paysages.

in any case, we have beautiful landscapes.

Captions 15-16, Fanny et Corrine - Leurs origines

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Notice how Corrine mentions Marseilles' beaux paysages (beautiful landscapes). The adjective beaux (beautiful) has fewer syllables than the noun paysages (landscapes), so beaux is placed before paysages.

Conversely, the adjective is usually placed after the noun if it has more syllables than does the noun. For example, you would say une voix horrible (a horrible voice); the noun voix (voice) has fewer syllables than the adjective horrible, so the noun comes first.

Le Journal tells the story of Claudia Rusch, a young Francophile who was one of the first to scramble over the falling Berlin Wall to join a friend on that memorable day, November 9th, 1989.

...escalade ce grillage insupportable qui les sépare.

...scales this unbearable fence which separates them.

Caption 23, Le Journal - Le mur de Berlin s'écroule

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Here, because the adjective insupportable (unbearable) has a greater number of syllables than the noun grillage (fence), the adjective goes last.

See? It's as easy as 1, 2, 3!