See here for the sklearn page about SVM, there you have a section for multiclass classification using SVM. You first have to convert your texts into a feature vector (numeric, if you wish you use SVM) If you should like to use bag of words you could use this SO question and this manual page of sklearn
You can use pre written python code to create BOW from you texts doing something like that - mind you, i geathered the relevant information for the OP - that was unclear and not compatible with SO strandarts, so you might need to work the code a bit for it to fit your excact usage.
>>> from sklearn.feature_extraction.text import CountVectorizer
>>> vectorizer = CountVectorizer()
>>> vectorizer
CountVectorizer(analyzer=...'word', binary=False, decode_error=...'strict',
dtype=<... 'numpy.int64'>, encoding=...'utf-8', input=...'content',
lowercase=True, max_df=1.0, max_features=None, min_df=1,
ngram_range=(1, 1), preprocessor=None, stop_words=None,
strip_accents=None, token_pattern=...'(?u)\\b\\w\\w+\\b',
tokenizer=None, vocabulary=None)
>>> corpus = [
... 'This is the first document.',
... 'This is the second second document.',
... 'And the third one.',
... 'Is this the first document?',
... ]
>>> X = vectorizer.fit_transform(corpus)
>>> X
<4x9 sparse matrix of type '<... 'numpy.int64'>'
with 19 stored elements in Compressed Sparse ... format>
Then you might need to convert x into a dense matrix (depends on sklearn version)
Then you could feed x into SVM model you can create like so
>>>>from sklearn import svm
>>> X = [[0], [1], [2], [3]]
>>> Y = [0, 1, 2, 3]
>>> clf = svm.SVC(gamma='scale', decision_function_shape='ovo')
>>> clf.fit(X, Y)
SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,
decision_function_shape='ovo', degree=3, gamma='scale', kernel='rbf',
max_iter=-1, probability=False, random_state=None, shrinking=True,
tol=0.001, verbose=False)
>>> dec = clf.decision_function([[1]])
>>> dec.shape[1] # 4 classes: 4*3/2 = 6
6
>>> clf.decision_function_shape = "ovr"
>>> dec = clf.decision_function([[1]])
>>> dec.shape[1] # 4 classes